Iran Nuclear Treaty Act This bill requires Senate approval of certain actions with respect to Iran's nuclear program. Specifically, the bill deems any agreement reached between the President and Iran relating to Iran's nuclear program to be a treaty that is subject to the advice and consent of the Senate. Further, the bill prohibits the President from (1) limiting the application of certain sanctions, or (2) refraining to apply such sanctions pursuant to an agreement unless the agreement is subject to the advice and consent of the Senate as a treaty.