The Faraday rotation caused by electronic transitions between the 4f and 5d states of Ce ions in paramagnetic CeF_3_ crystals is calculated. The crystal field is an important perturbation on the energy levels. An external magnetic field, together with an additive magnetic field introduced phenomenologically in our paper, would spilt every 4f state into two sublevels. The dipole transitions between these sublevels, and 5d states induce the Faradap effect. The Verdet constant at 0.6328 um in the temperature range of 60-300K is obtained. It is shown that our calculation is in good agreement with experiment.