We demonstrate a silicon photonic dual-polarization phase retrieval receiver. The receiver recovers phase from intensity-only measurements without a local oscillator or transmitted carrier. We design silicon waveguides providing long delays and microring resonators with large dispersion to enable symbol-to-symbol interference and dispersive projection in the phase retrieval algorithm. We retrieve the full field of a polarization-division multiplexed 30-GBd QPSK and 20-GBd 8QAM signals over 80 km of SSMF.