We developed a self-consistent three-dimensional reference interaction site model integral equation theory with the molecular hypernetted chain closure (SC-3D-RISM/HNC) for studying thermochemistry of solvation of ionic solutes in a polar molecular solvent. It is free from the inconsistency in the positions of the ion-solvent site distribution peaks, peculiar to the conventional RISM/HNC approach and improves the predictions for the solvation thermodynamics. The SC-3D-RISM treatment can be readily generalized to the case of finite ionic concentrations, including the consistent dielectric corrections to provide a consistent description of the dielectric properties of ion-molecular solution. The proposed theory is tested for hydration of the Na+ and Cl- ions in ambient water at infinite dilution. An improved agreement of the ion hydration structure and thermodynamics with molecular simulation results is found as compared to the conventional RISM/HNC treatment.