EXHIBIT 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We have issued our report dated March 24, 2015 (except for the effects of the restatement described in Note 1A, as to which the date is May 20, 2015), with respect to the consolidated financial statements included in the Annual Report of Cellectar Biosciences, Inc. on Form 10-K/A for the year ended December 31, 2014. We hereby consent to the incorporation by reference of said report in the Registration Statements of Cellectar Biosciences, Inc. on Form S-3 (File No. 333-201429) and on Forms S-8 (File No. 333-195255 and File No. 333-164398).

/s/ GRANT THORNTON LLP

Chicago, Illinois

May 20, 2015