Generating polarization-entangled photon pairs on chip is generally complicated by the birefringence of waveguides. In this work, we propose a technique that uses waveguide birefringence and lends itself to simple device designs. The technique relies on two orthogonal spontaneous four-wave mixing processes. We employ the full quantum optics theory and dispersion analysis, and show that the technique can produce highly entangled states, with concurrence as high as 0.976 and covering the entire C-band.