A theoretical treatment of the Faraday effect has been made with respect to Cd_<1-χ>Mn_χTe films prepared by ionized-cluster beams. The Faraday rotation spectra are calculated.taking account of a broadening parameter Γ of exciton absorption in a nondegenerate second order perturbation theory. The calculated spectra are compared with the experimental data of Cd_<1-χ>Mn_χTe films. The results reveal that the thermal broadening of exciton absorption is due to the scattering of an exciton by longitudinal optical (LO) phonons.