Spin pumping refers to the microwave-driven spin current injection from a ferromagnet into the adjacent target material. We theoretically investigate the spin pumping into superconductors by fully taking account of impurity spin-orbit scattering that is indispensable to describe diffusive spin transport with finite spin diffusion length. We calculate temperature dependence of the spin pumping signal and show that a pronounced coherence peak appears immediately below the superconducting transition temperature T-c, which survives even in the presence of the spin-orbit scattering. The phenomenon provides us with a new way of studying the dynamic spin susceptibility in a superconducting thin film. This is contrasted with the nuclear magnetic resonance technique used to study a bulk superconductor.