The spaceborne P-band fully polarimetric synthetic aperture radar (SAR) working system is highly susceptible to the scintillation effects induced by ionospheric irregularities due to its low carrier frequency. The scintillation phase error (SPE) is a dominant factor that leads to azimuth decorrelation. The aperture-dependent and spatial-varying characteristics of the SPE promote the complexity of the SPE estimation and compensation. In this paper, a methodology is described that compensates the SPE by estimating the Faraday rotation (FR) angle from fully polarimetric SAR data. The multi-aperture scheme is adopted, including the sub-aperture FR estimation, multi-aperture splicing, and overall compensation, to take the complicated characteristics of the aperture-dependent and spatial-varying SPE into account. The methodology is finally validated on simulated data derived from the airborne P-band SAR real data, and compared with an existing method. The new method does not need prior knowledge of the ionospheric height. Furthermore, its performance is investigated in relation to several key factors in different simulation conditions.