Digital optical phase conjugation (DOPC) is an emerging technique for focusing light through or within scattering media such as biological tissue. Since DOPC systems are based on time reversal, they benefit from collecting as much information about the scattered light as possible. However, existing DOPC techniques record and subsequently phase-conjugate the scattered light in only a single-polarization state, limited by the operating principle of spatial light modulators. Here, we develop the first, to the best of our knowledge, full-polarization DOPC system that records and phase-conjugates scattered light along two orthogonal polarizations. When focusing light through thick scattering media, such as 2 mm and 4 mm-thick chicken breast tissue, our full-polarization DOPC system on average doubles the focal peak-to-background ratio achieved by single-polarization DOPC systems and improves the phase-conjugation fidelity.