WARRANT TO PURCHASE STOCK

Exhibit 4.1

THIS WARRANT AND THE SHARES ISSUABLE HEREUNDER HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE OFFERED, SOLD, PLEDGED OR OTHERWISE TRANSFERRED EXCEPT IN ACCORDANCE WITH APPLICABLE LAW.

WARRANT TO PURCHASE STOCK

THIS WARRANT CERTIFIES THAT, for good and valuable consideration, the receipt of which is hereby acknowledged, SQUARE 1 BANK or its assignee (“Holder”) is entitled to purchase the number of fully paid and nonassessable shares of the class of securities (the “Shares”) of the corporation (the “Company”) at the initial exercise price per Share (the “Warrant Price”) all as set forth above and as adjusted pursuant to Article 2 of this warrant, subject to the provisions and upon the terms and conditions set forth in this warrant.

ARTICLE 1

EXERCISE

1.1 Method of Exercise. Holder may exercise this warrant by delivering this warrant and a duly executed Notice of Exercise in substantially the form attached as Appendix 1 to the principal office of the Company. Unless Holder is exercising the conversion right set forth in Section 1.2, Holder shall also deliver to the Company a check for the aggregate Warrant Price for the Shares being purchased.

1.2 Conversion Right. In lieu of exercising this warrant as specified in Section 1.1, Holder may from time to time convert this warrant, in whole or in part, into a number of Shares determined by dividing (a) the aggregate fair market value of the Shares or other securities otherwise issuable upon exercise of this warrant minus the aggregate Warrant Price of such Shares by (b) the fair market value of one Share. The fair market value of the Shares shall be determined pursuant to Section 1.3.

1.3 Fair Market Value. If the Shares are traded regularly in a public market, the fair market value of the Shares shall be the closing price of the Shares reported for the business day immediately before Holder delivers its Notice of Exercise to the Company. If the Shares are not regularly traded in a public market, the Board of Directors of the Company shall determine fair market value in its reasonable good faith judgment.

1.4 Delivery of Certificate and New Warrant. Reasonably promptly after Holder exercises or converts this warrant, the Company shall deliver to Holder certificates for the Shares acquired and, if this warrant has not been fully exercised or converted and has not expired, a new warrant representing the Shares not so acquired.

1.5 Replacement of Warrants. On receipt of evidence reasonably satisfactory to the Company of the loss, theft, destruction or mutilation of this warrant and, in the case of loss, theft or destruction, on delivery of an indemnity agreement reasonably satisfactory in form and amount to the Company or, in the case of mutilation, on surrender and cancellation of this warrant, the Company at its expense shall execute and deliver, in lieu of this warrant, a new warrant of like tenor.

1.6 Repurchase on Sale, Merger, or Consolidation of the Company.

1.6.1 “Acquisition.” For the purpose of this warrant, “Acquisition” means (a) any sale, license, or other disposition of all or substantially all of the assets (including intellectual property) of the Company, or (b) any reorganization, consolidation, merger or sale of the voting securities of the Company or any other transaction where the holders of the Company’s securities before the transaction beneficially own less than 50% of the outstanding voting securities of the surviving entity after the transaction.

1.6.2 Assumption of Warrant. If upon the closing of any Acquisition the successor entity assumes the obligations of this warrant, then this warrant shall be exercisable for the same securities, cash, and property as would be payable for the Shares issuable upon exercise of the unexercised portion of this warrant as if such Shares were outstanding on the record date for the Acquisition and subsequent closing. The Warrant Price shall be adjusted accordingly.

1.6.3 Nonassumption. If upon the closing of any Acquisition the successor entity does not assume the obligations of this warrant and Holder has not otherwise exercised this warrant in full, then this warrant shall be deemed to have been automatically converted pursuant to Section 1.2 and thereafter Holder shall participate in the Acquisition on the same terms as other holders of the same class of securities of the Company.

1.7 Amount of Warrant Shares. This warrant shall be exercisable for the number of Shares (before giving effect to any adjustment made in accordance with Article 2) equal to the quotient of (a) 3% of the principal amount of the Credit Extension made on the Issue Date under that certain Loan and Security Agreement between the Company and Square 1 Bank, dated on or about May 28, 2014, as it may be amended from time to time, over (b) the Initial Exercise Price.

1.8 Initial Exercise Price. The Initial Exercise Price shall be the closing price of the Company’s common stock on the Issue Date.

ARTICLE 2

ADJUSTMENTS TO THE SHARES

2.1 Stock Dividends, Splits, Etc. If the Company declares or pays a dividend on its common stock payable in common stock, or other securities, or subdivides the outstanding common stock into a greater amount of common stock, then upon exercise of this warrant, for each Share acquired, Holder shall receive, without cost to Holder, the total number and kind of securities to which Holder would have been entitled had Holder owned the Shares of record as of the date the dividend or subdivision occurred.

2.2 Reclassification, Exchange or Substitution. Upon any reclassification, exchange, substitution, or other event that results in a change of the number and/or class of the securities issuable upon exercise or conversion of this warrant, Holder shall be entitled to receive, upon exercise or conversion of this warrant, the number and kind of securities and property that Holder would have received for the Shares if this warrant had been exercised immediately before such reclassification, exchange, substitution, or other event. The Company or its successor shall reasonably promptly issue to Holder a new warrant for such new securities or other property. The new warrant shall provide for adjustments which shall be as nearly equivalent as may be practicable to the adjustments provided for in this Article 2 including, without limitation, adjustments to the Warrant Price and to the number of securities or property issuable upon exercise of the new warrant. The provisions of this Section 2.2 shall similarly apply to successive reclassifications, exchanges, substitutions, or other events.

2.3 Adjustments for Combinations, Etc. If the outstanding Shares are combined or consolidated, by reclassification or otherwise, into a lesser number of shares, the Warrant Price shall be proportionately increased. If the outstanding Shares are combined or consolidated, by reclassification or otherwise, into a greater number of shares, the Warrant Price shall be proportionately decreased.

2.4 [Reserved].

2.5 Certificate as to Adjustments. Upon each adjustment of the Warrant Price, the Company at its expense shall reasonably promptly compute such adjustment, and furnish Holder with a certificate of its Chief Business Officer setting forth such adjustment and the facts upon which such adjustment is based. The Company shall, upon written request, furnish Holder a certificate setting forth the Warrant Price in effect upon the date thereof and the series of adjustments leading to such Warrant Price.

2.6 Fractional Shares. No fractional Shares shall be issuable upon exercise or conversion of this warrant, and the number of Shares to be issued shall be rounded down to the nearest whole Share. If a fractional share interest arises upon any exercise or conversion of the warrant, the Company shall eliminate such fractional share interest by paying Holder the amount computed by multiplying the fractional interest by the fair market value of a full Share.

ARTICLE 3

REPRESENTATIONS AND COVENANTS OF THE COMPANY

3.1 Representations and Warranties.

(a) The Company hereby represents and warrants to the Holder as follows:

(i) All Shares which may be issued upon the exercise of the purchase right represented by this warrant, and all securities, if any, issuable upon conversion of the Shares, shall, upon issuance, be duly authorized, validly issued, fully paid and nonassessable, and free of any liens and encumbrances except for restrictions on transfer provided for herein or under applicable federal and state securities laws.

(ii) The Company’s capitalization table attached to this warrant is true and complete as of the Issue Date.

(b) The Holder hereby represents and warrants to the Company as follows:

(i) The Holder is acquiring this warrant for its own account for investment and not with a view to, or for sale in connection with, any distribution thereof; nor with any present intention of distributing or selling the same; and the Holder has no present or contemplated agreement, undertaking, arrangement, obligation, indebtedness or commitment providing for the disposition thereof;

(ii) The Holder is an “accredited investor” as defined in Rule 501(a) under the Securities Act of 1933, as amended; and

(iii) The Holder has made such inquiry concerning the Company and its business and personnel as it has deemed appropriate and the Holder has sufficient knowledge and experience in finance and business that it is capable of evaluating the risks and merits of its investment in the Company.

3.2 Notice of Certain Events. The Company shall provide Holder with not less than 10 days’ prior written notice, including a description of the material facts surrounding, any of the following events: (a) declaration of any dividend or distribution upon its common stock, whether in cash, property, stock, or other securities and whether or not a regular cash dividend; (b) effecting any reclassification or recapitalization of common stock; or (c) the merger or consolidation with or into any other corporation, or sale, lease, license, or conveyance of all or substantially all of its assets, or liquidation, dissolution or winding up.

3.3 Information Rights. At any time when the Company is not complying with the periodic reporting requirements of the Securities Exchange Act of 1934, as amended, and so long as the Holder holds this warrant and/or any of the Shares, the Company shall deliver to the Holder (a) reasonably promptly after mailing, copies of all communiques to the shareholders of the Company, (b) within one hundred eighty (180) days after the end of each fiscal year of the Company, the annual audited financial statements of the Company certified by independent public accountants of recognized standing and (c) within forty-five (45) days after the end of each of the first three quarters of each fiscal year, the Company’s quarterly, unaudited financial statements.

ARTICLE 4

MISCELLANEOUS

4.1 Term: Exercise Upon Expiration. This warrant is exercisable in whole or in part, at any time and from time to time on or before the Expiration Date set forth above. If this warrant has not been exercised prior to the Expiration Date, this warrant shall be deemed to have been automatically exercised on the Expiration Date by “cashless” conversion pursuant to Section 1.2.

4.2 Legends. This warrant and the Shares (and the securities issuable, directly or indirectly, upon conversion of the Shares, if any) shall be imprinted with a legend in substantially the following form:

THIS SECURITY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE OFFERED, SOLD, PLEDGED OR OTHERWISE TRANSFERRED EXCEPT IN ACCORDANCE WITH APPLICABLE LAW.

4.3 Compliance with Securities Laws on Transfer. This warrant and the Shares issuable upon exercise of this warrant may not be transferred or assigned in whole or in part without compliance with applicable federal and state securities laws by the transferor and the transferee (including, without limitation, the delivery of investment representation letters and legal opinions reasonably satisfactory to the Company, as reasonably requested by the Company). The Company shall not require Holder to provide an opinion of counsel if the transfer is to an affiliate of Holder or if there is no material question as to the availability of current information as referenced in Rule 144(c), Holder represents that it has complied with Rule 144(d) and (e) in reasonable detail, the selling broker represents that it has complied with Rule 144(f), and the Company is provided with a copy of Holder’s notice of proposed sale. The Company shall not require Holder to provide an investment representation letter or an opinion of counsel if the transfer is to a holding company that controls Holder, or to a trust created by such holding company for the purpose of maintaining warrants and other equity securities on behalf of Holder.

4.4 Transfer Procedure. Subject to the provisions of Section 4.3, Holder may transfer all or part of this warrant (this warrant, together with any warrants issued upon any permitted transfer hereunder are referred to herein collectively as the “Warrants”) or the Shares issuable upon exercise of this warrant by giving the Company notice of the portion of the warrant being transferred setting forth the name, address and taxpayer identification number of the transferee and surrendering this warrant to the Company for reissuance to the transferee(s) (and Holder, if applicable). No surrender or reissuance shall be required if the transfer is to an affiliate of Holder.

4.5 Notices. All notices and other communications from the Company to the Holder, or vice versa, shall be deemed delivered and effective when given personally or mailed by first-class registered or certified mail, postage prepaid, at such address as may have been furnished to the Company or the Holder, as the case may be, in writing by the Company or such Holder from time to time. All notices to the Holder shall be addressed as follows:

Square 1 Bank

Attn: Warrant Administrator

406 Blackwell Street, Suite 240

Crowe Building

Durham, NC 27701

All notices to the Company shall be addressed as follows:

Evoke Pharma, Inc.

Attn: Matt D’Onofrio

505 Lomas Santa Fe Drive

Suite 270

Solana Beach, CA 92075

With a copy to:

Latham & Watkins LLP

Attn: Cheston Larson

12670 High Bluff Drive

San Diego, CA 92130

4.6 Amendments. This warrant and any term hereof may be changed or waived only by an instrument in writing signed by the Company and the holders of Warrants exercisable for a majority of the total number of Shares then issuable pursuant to all Warrants. Any change or waiver effected in accordance with this Section 4.6 shall be binding upon each holder of Warrants.

4.7 Attorneys’ Fees. In the event of any dispute between the parties concerning the terms and provisions of this warrant, the party prevailing in such dispute shall be entitled to collect from the other party all costs incurred in such dispute, including reasonable attorneys’ fees.

4.8 Governing Law. This warrant shall be governed by and construed in accordance with the laws of the State of California, without giving effect to its principles regarding conflicts of law.

4.9 No Rights as Shareholder. Until the exercise of this warrant, the Holder shall not have or exercise any rights by virtue hereof as a shareholder of the Company.

[Signature Page Follows]

IN WITNESS WHEREOF, the undersigned has executed this Warrant to Purchase Stock as of the date set forth above.

[Signature Page to Warrant to Purchase Stock]

APPENDIX 1

NOTICE OF EXERCISE

1. The undersigned hereby elects to purchase              shares of the common stock of EVOKE PHARMA, INC. pursuant to the terms of the attached warrant, and tenders herewith payment of the purchase price of such shares in full.

1. The undersigned hereby elects to convert the attached warrant into shares in the manner specified in the warrant. This conversion is exercised with respect to              of the shares covered by the warrant.

[Strike paragraph that does not apply.]

2. Please issue a certificate or certificates representing said shares in the name of the undersigned or in such other name as is specified below:

Square 1 Bank

Attn: Warrant Administrator

406 Blackwell Street, Suite 240

Fowler Building

Durham, NC 27701

3. The undersigned represents it is acquiring the shares solely for its own account and not as a nominee for any other party and not with a view toward the resale or distribution thereof except in compliance with applicable securities laws, and hereby reaffirms the representations and warranties set forth in Sections 3.1(b), 4.2, 4.3 and 4.4 of the attached warrant.