We consider the scattering of brane fields due to t-channel massive graviton exchanges in the Randall-Sundrum model. The eikonal amplitude is analytically calculated and both differential and total neutrino-nucleon cross sections are estimated. The event rate of quasi-horizontal air showers induced by cosmic neutrinos, which can be detected at the Pierre Auger Observatory, is presented for two different fluxes of cosmogenic neutrinos.