Polarization sensitive quantum optical coherence tomography (PS-QOCT) is used to characterize birefringence, scattering/absorption and path length differences in a flat transparent plastic sample. In this Letter, we present the first, to the best of our knowledge, experimental technique of PS-QOCT imaging and characterization of a birefringent material. Polarization sensitive coincidence rate of the entangled photons measured for each pixel and the 2D cross-sectional images are reconstructed. The technique described in this work has many potential applications in the characterization of micro and nano structures, including biological samples.