The non-oscillating part of the magnetic moment field (called the inverse Faraday effect (IFE) for this field from a circularly polarized wave in a medium) is calculated for the interaction of an elliptically polarized wave with a weakly ionized magnetized plasma in a kinetic theory model and with unmagnetized Vlasov plasmas. For a weakly ionized magnetized plasma, the induced field increases with both temperature and ambient magnetic field. For an unmagnetized plasma, it increases parabolically with temperature. The induced magnetic field is found to vary parabolically with temperature in the case of an unmagnetized Vlasov plasma.