We present complementary methods for calibrating the dual-polarization feed of a ground-based tracking antenna used for ionospheric measurements. Several calibration parameters are defined which describe the state of the measurement equipment. These key parameters then form a transformational Mueller matrix which may be used to remove system bias in data received from known beacons. Several strategies are developed to quantify these time-dependent distortions for the Green Bank 140′ diameter antenna and receiver, although these methods could be applied to other similar systems. One approach quantifies the receiver biases in terms of amplitude and gain differentials. This is accomplished by measuring polarimetric differences between channels using a test signal with a known amplitude and phase. Due to variations over time periods on the scale of a beacon track, this procedure is most effective when the calibration signal is injected concurrently with the beacon measurements. To determine antenna feed distortion, including cross-polarization and ellipticity, data is recorded from an external celestial source. An example shows the effectiveness of this calibration technique by comparing calibrated data to data without correction. Error estimates of the calibration parameters in the example establish an upper bound of 0.22 TEC units for measurements at 150 MHz along track.