Magneto-optical effect in the room-temperature ionic liquid 1-butyl-3-methylimidazolium tetrachloroferrate ([bmim][FeCl4]) is reported. Faraday rotation angle (theta(F)) shows a monotonic variation as a function of wavelength in the wavelength range from visible to near-infrared. A linear dependence of theta(F) on magnetic fields is in accord with the paramagnetism of [bmim][FeCl4]. The Verdet constant calculated from theta(F) for the molecule-based magnetic ionic liquid is comparable to those in rare-earth aluminum garnets.