This Letter demonstrates spin wave resonance (SWR) owing to the gyromagnetic effect by propagating a Rayleigh-type surface acoustic wave (R-SAW) through ferromagnetic thin films. The SWR amplitude in a NiFe film shows a higher-order frequency variation than in a magnetoelastic Ni film. This frequency dependence is well understood in terms of the presence of a gyromagnetic field attributable to the local lattice rotation in the R-SAW. From the frequency dependence of the SWR amplitude, the gyromagnetic SWR could be separated from another SWR caused by a magnetoelastic effect of the ferromagnet.