Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the reference to our firm under the caption “Experts” in this Registration Statement (Form S-3) and related Prospectus of Cencora, Inc. for the registration of its common stock, preferred stock, debt securities, depositary shares, warrants, purchase contracts and units and to the incorporation by reference therein of our reports dated November 26, 2024, with respect to the consolidated financial statements and schedule of Cencora, Inc. and subsidiaries, and the effectiveness of internal control over financial reporting of Cencora, Inc. and subsidiaries, included in its Annual Report (Form 10-K) for the year ended September 30, 2024, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

Philadelphia, Pennsylvania

November 26, 2024