We examine the reversible adsorption of spherical solutes on a random site surface in which the adsorption sites are uniformly and randomly distributed on a substrate. Each site can be occupied by one solute provided that the nearest occupied site is at least one diameter away. The model is characterized by the site density and the bulk phase activity of the adsorbate. We develop a general statistical mechanical description of the model, and we obtain exact expressions for the adsorption isotherms in limiting cases of large and small activity and site density, particularly for the one-dimensional version of the model. We also propose approximate isotherms that interpolate between the exact results. These theories are in good agreement with numerical simulations of the model in two dimensions.