The stabilization problem for the Schr¨odinger equation with an input time delay is considered from the view of system equivalence. First, a linear transform from the original system into an exponentially stable system with arbitrary decay rate, also called “target system”, is introduced. The linear transform is constructed via a kind of Volterra-type integration with singular kernels functions. As a result, a feedback control law for the original system is obtained. Secondly, a linear transform from the target system into the original closed-loop system is derived. Finally, the exponential stability with arbitrary decay rate of the closed-loop system is obtained through the established equivalence between the original closed-loop system and the target one. The authors conclude this work with some numerical simulations giving support to the results obtained in this paper.