Exhibit 31.3

CERTIFICATIONS

I, Vincent J. Angotti, certify that:

1. I have reviewed this annual report on Form 10-K/A of AcelRx Pharmaceuticals, Inc.;

2. Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;

Date: April 17, 2020

/s/ Vincent J. Angotti

Vincent J. Angotti

Chief Executive Officer

(Principal Executive Officer)