Calculations of the Faraday rotation and ellipticity spectra at photon energies between 0.98 and 3.50 eV (wavelengths between 1260 and 360 nm) resulting from Ce ions in the Ce-substituted yttrium iron garnets based on the quantum theory are presented. The Faraday effect contributed by the Ce ions is caused mainly by the intra-ionic electrical dipole transitions between the 4f and 5d configurations. The crystal field (CF) and the superexchange interaction are two crucial factors in determining the Faraday effect contributed by the Ce sublattice. The energy differences between the lowest and the second CF-split 5d levels and the lowest CF-split 4f level are 1.36 eV and 3.10 eV, respectively. Therefore there are anomalous rotatory dispersions at about 1.36 eV and 3.10 eV. The difference between the transition intensities for the right- and left-handed circularly polarized light between the lowest CF-split 5d level and the ground state is negative. while the corresponding value for the transition between the second CF-split 5d level and the ground state is positive. So the Faraday rotation is positive over the whole photon energy region between 1.36 and 3.10 eV and is negative outside this region. The calculated spectra are in good agreement with experiment.