Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in this Registration Statement on Form S-1 and related Prospectus, of our report dated March 17, 2025, with respect to the financial statements of Acurx Pharmaceuticals, Inc. as of December 31, 2024 and 2023, and for the years then ended, which report is included in the Annual Report on Form 10-K of Acurx Pharmaceuticals, Inc. for the year ended December 31, 2024, filed with the Securities and Exchange Commission. Our audit report includes an explanatory paragraph relating to Acurx Pharmaceuticals, Inc.’s ability to continue as a going concern.

We also consent to the reference to our firm under the caption “Experts.”

/s/ CohnReznick LLP

Parsippany, New Jersey

July 14, 2025