Cd_(1-x-y)Mn_xHg_yTe single crystals were grown by using the vertical Bridgman method. The Verdet constant was evaluated as a function of the photon energy by using the result for the Faraday rotation. Th Verdet curve was well fitted by using a single-oscillator method and shifted downward at y≥0 due to the exchange interaction. The Faraday rotation decreased linearly with increasing magnetic field from 0 KG to 8 KG.