EXHIBIT 23.1

Consent of Independent Registered Public Accounting Firm

We have issued our report dated March 11, 2016, with respect to the consolidated financial statements included in the Annual Report of Cellectar Biosciences, Inc. on Form 10-K for the year ended December 31, 2015. We consent to the incorporation by reference of said report in the Registration Statements of Cellectar Biosciences, Inc. on Forms S-3 (File No. 333-208189 and File No. 333-201429) and on Forms S-8 (File No. 333-195255 and File No. 333-164398).

/s/ GRANT THORNTON LLP

Appleton, Wisconsin

March 11, 2016