Faraday rotation (FR) is one of the main error sources for passive microwave remote sensing from space especially in frequencies less than or equal to 10.7 GHz. In this paper, Faraday rotation correction for the vertical brightness temperature at L band and the third Stokes parameter brightness temperature at 10.7 GHz are discussed. Two approaches are studied to remove the influence of FR: correction by auxiliary data and correction by polarimetric mode. At 1.4 GHz, correction by polarimetric mode performs better than correction by auxiliary data. At 10.7 GHz, correction by auxiliary data is feasible while polarimetric mode correction becomes invalid. We propose a new method of using TEC data released by international GNSS service (IGS) for correction. It has been proved that the residual correction errors are reduced. IGS data method greatly improves the correction accuracy