A linearized RISM technique is developed to treat free energies of hydrated ions. The solvent response on the solute is calculated with the introduction of an empirical repulsive bridge function. The solvent electrostatic potential is approximated by a linear dependence on the solute charge. The approximating coefficients are derived by fitting the electrostatic energy of solvent, that is in turns computed by the charging procedure. For a series of monovalent polyatomic cations and anions the method provides free energies deviating by few percent from the experimental data.