Antenna arrays with adaptive filtering can protect the integrity and functionality of global navigation satellite system (GNSS) receivers against interference. However, a major problem with existing adaptive array processing algorithms is that they cause phase distortions and introduce bias errors into the carrier phase measurement, limiting high-precision applications. In this paper, a robust phase compensation technique is proposed to reduce the phase distortion. First, a phase bias detection method is developed to trigger the phase compensation technique. Then, the phase bias is estimated using a robust estimation method and compensated for in the GNSS receiver. The proposed technique operates in real time and causes no processing delay, while requiring only a minor modification to existing GNSS receivers. This technique is applied to the power inversion adaptive antenna, and can also be extended to a wide variety of adaptive antennas. The simulation experiments verify the applicability of the proposed technique and also confirm its superiority over existing techniques.