The Randall-Sundrum model with a small curvature is considered in which five-dimensional Planck scale lies
in the TeV region. The cross sections for interactions of ultra-high energy cosmic neutrinos with nucleons are calculated.
It is shown that effects related with Kaluza-Klein graviton excitations can be detected in deeply penetrating inclined air
showers induced by these neutrinos. The expected number of the inclined air showers at the Auger Observatory is
estimated as a function of two parameters of the model.