Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference, in the Prospectus constituting a part of this Registration Statement on Form S-3, of our reports dated March 16, 2020 relating to the consolidated financial statements and the effectiveness of internal control over financial reporting of AcelRx Pharmaceuticals, Inc. appearing in AcelRx Pharmaceuticals, Inc.'s Annual Report on Form 10-K for the year ended December 31, 2019.

We also consent to the reference to us under the caption “Experts” in the Prospectus.

/s/ OUM & CO. LLP

San Francisco, California

June 12, 2020