The magnitude and radial profiles of non-inductive currents driven by fast magnetosonic waves in tokamaks have been calculated directly from the wave induced quasi-linear flux in a toroidal geometry and a Green's function for the current. An expression for the quasi-linear flux has been derived that accounts for coupling between modes in the spectrum of waves launched from the antenna. A Fokker-Planck code for the Green's function and a full wave code for the electric field in the quasi-linear flux are used to evaluate the current in a specified toroidal geometry