Origin of polarization sensitivity of the silicon cross-slot waveguide (SCSW) is analyzed. The effective refractive indices as well as the single-mode-operation conditions of SCSWs for different polarization states are calculated. A single-mode SCSW can be polarization-insensitive if its structure is designed dedicated. A polarization-independent micro-ring resonator with 3.7μm radius based on a polarization-insensitive SCSW is proposed and simulated. The polarization-independent working bandwidth of the micro-ring resonator is about 64 nm, and the free spectral range is about 35 nm.