Satellite-based quantum key distribution (QKD) is one of the effective solutions for building a global-scale quantum network. For practical satellite-based polarization-encoding QKD systems, the polarization degradation introduced by the single-mode fiber and the relative rotation between satellites and ground stations will lead to a decrease in the polarization performance and need to be compensated. In this work, we propose two novel on-orbit satellite-to-ground joint polarization measurement and compensation methods, which can ensure high polarization fidelity while effectively saving hardware resources and reducing costs. By establishing a polarization compensation model and performing theoretical analysis, combined with desktop experimental verification, we demonstrated the effectiveness of the satellite-to-ground joint polarization compensation and achieved a low quantum bit error rate below 0.3% after background removal. The presented polarization compensation laid the foundation for the subsequent applications in satellite-based QKD and satellite-based quantum networks.