We demonstrate the generation of alternating spin current (SC) via spin-rotation coupling (SRC) using a surface acoustic wave (SAW) in a Cu film. Ferromagnetic resonance caused by injecting SAWs was observed in a Ni-Fe film attached to a Cu film, with the resonance further found to be suppressed through the insertion of a SiO_{2} film into the interface. The intensity of the resonance depended on the angle between the wave vector of the SAW and the magnetization of the Ni-Fe film. This angular dependence is explicable in terms of the presence of spin transfer torque from a SC generated via SRC.