Exhibit 5.1

Pillsbury Winthrop Shaw Pittman LLP

Houston | London | Los Angeles | New York | Northern Virginia | Orange County | Sacramento | San Diego | San Diego North County | San Francisco | Shanghai | Silicon Valley | Tokyo | Washington, DC

March 18, 2020

Acer Therapeutics Inc.

One Gateway Center, Ste. 351, 300 Washington St.

Newton, MA 02458

Re: Registration Statement on Form S-8

Ladies and Gentlemen:

We are acting as counsel for Acer Therapeutics Inc., a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-8 (the “Registration Statement”) relating to the registration under the Securities Act of 1933 (the “Act”) of 403,807 shares of the Company’s common stock, $0.0001 par value per share (the “Shares”), issuable pursuant to the Company’s 2018 Stock Incentive Plan (the “Plan”).

We have reviewed and are familiar with such corporate proceedings and other matters as we have deemed relevant or necessary for the opinions expressed in this letter. Based upon the foregoing, we are of the opinion that the Shares have been duly authorized and, when issued and sold in accordance with the Plan, will be validly issued, fully paid and nonassessable. The opinions set forth in this letter are limited to the General Corporation Law of the State of Delaware, as in effect on the date hereof.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

Very truly yours,

/s/ Pillsbury Winthrop Shaw Pittman LLP