Rainfall has long been associated with damping of short surface gravity waves. A theory is presented which uses a thin rain-induced turbulent surface layer to explain the enhanced attenuation. In the presence of a thin turbulent surface layer, the e-folding attenuation time for the 30-cm wavelength surface gravity waves needed for remote sensing of the ocean surface using synthetic aperture radar (SAR) is reduced from several minutes to several seconds. This explains the observation of low SAR radar return from regions of high rainfall. Longer wavelengths are also affected depending on the strength of the mixing and the thickness of the turbulent layer.