This paper presents the device design and performance analysis of a novel design of planar optical cross-connect (OXC) using nematic liquid crystal (NLC) waveguides. It employs N × N switching matrix in cross-bar fabric. In each unit cell, the input light is set in either the transverse electric (TE) mode or the transverse magnetic (TM) mode by electrically reorienting the NLC in the waveguide. The light then enters a passive waveguide and is routed to different paths depending on the polarization state (TE/TM mode). A sample device of 8 × 8 OXC is analyzed for performance estimation, which predicts a maximum on-chip insertion loss of 3 dB, an average cross-talk of -40 dB, ~1 ms switching time, and 2 mm × 2 mm footprint. The proposed OXC is unique in the switching mechanism of polarization-dependent routing and allows non-blocking switching with high compactness and broad bandwidth. It is potential for optical circuit switching in data centers and optical communication networks.