We propose a simple theoretical formula for describing the refractive indices in binary liquid mixtures containing salt ions. Our theory is based on the Clausius-Mossotti equation; it gives the refractive index of the mixture in terms of the refractive indices of the pure liquids and the polarizability of the ionic species, by properly accounting for the volume change upon mixing. The theoretical predictions are tested by extensive experimental measurements of the refractive indices for water-acetonitrile-salt systems for several liquid compositions, different salt species, and a range of salt concentrations. Excellent agreement is obtained in all cases, especially at low salt concentrations, with no fitting parameters. A simplified expression of the refractive index for low salt concentration is also given, which can be the theoretical basis for determination of salt concentration using refractive index measurements.