Exhibit 99.1

ACURX PHARMACEUTICALS, INC. announces pricing of $15 Million

underwritten INITIAL public offering of common stock

STATEN ISLAND, N.Y., June 25, 2021 — Acurx Pharmaceuticals, Inc. (Nasdaq: ACXP) (the “Company”), a clinical stage biopharmaceutical company developing a new class of antibiotics for difficult-to-treat bacterial infections, today announced the pricing of an underwritten initial public offering of 2,500,000 newly-issued shares of its common stock at a price of $6.00 per share. The gross proceeds to the Company from the offering are expected to be approximately $15 million before deducting underwriting discounts and commissions and estimated offering expenses payable by the Company. The Company has also granted to the underwriters of the offering a 45-day option to purchase up to an additional 375,000 shares of common stock to cover over-allotments in connection with the offering. The shares are expected to begin trading on June 25, 2021 on the Nasdaq Capital Market under the ticker symbol “ACXP.” The offering is expected to close on June 29, 2021, subject to customary closing conditions.

Alexander Capital L.P. is acting as lead book-running manager for the offering. Network 1 Financial Securities, Inc. is acting as co-manager.

The Company intends to use the net proceeds from this offering (i) to complete the Phase 2b clinical trial of ibezapolstat in patients with Clostridium difficile Infections, (ii) to complete pre-clinical development of ACX-375C and (iii) for general corporate purposes, which may include, without limitation, expenditures relating to research, development and clinical trials other than those specified above, manufacturing, capital expenditures, hiring additional personnel, acquisitions of new technologies or products, the payment, repayment, refinancing, redemption or repurchase of existing or future indebtedness, obligations or capital stock, and working capital.

The offering is being made only by means of a prospectus forming a part of the registration statement on Form S-1, as amended (File No. 333- 256516), previously filed with the Securities and Exchange Commission on June 11, 2021 and declared effective on June 24, 2021. Copies of such prospectus, when available, may be obtained from: Alexander Capital, L.P., 17 State Street, New York, New York 10014, (212) 687-5650, info@alexandercapitallp.com.

This press release does not constitute an offer to sell or the solicitation of an offer to buy any securities of the Company being offered, and shall not constitute an offer, solicitation or sale of any security in any state or jurisdiction in which such offer, solicitation or sale would be unlawful prior to registration or qualification under the securities laws of any such state or jurisdiction.

About Acurx Pharmaceuticals, Inc.

Acurx Pharmaceuticals is a clinical stage biopharmaceutical company focused on developing new antibiotics for difficult to treat infections. The Company’s approach is to develop antibiotic candidates that target the DNA polymerase IIIC enzyme and its R&D pipeline includes early stage antibiotic candidates that target other Gram-positive bacteria, including Methicillin-Resistant Staphylococcus aureus (MRSA), Vancomycin-Resistant Enterococcus (VRE) and Penicillin-Resistant Streptococcus pneumoniae (PRSP). For more information, please visit: www.acurxpharma.com.

Investor Contact:

David P. Luci, President and Chief Executive Officer

Acurx Pharmaceuticals, Inc.

Phone: (917) 533-1469

davidluci@acurxpharma.com