Superconducting-nanowire single photon detectors (SNSPDs) are able to reach near-unity detection efficiency in the infrared spectral range. However, due to the intrinsic asymmetry of nanowires, SNSPDs are usually very sensitive to the polarization of the incident radiation, their responsivity being maximum for light polarized parallel to the nanowire length (transverse-electric (TE) polarization). Here, we report on the reduction of the polarization sensitivity obtained by capping NbN-based SNSPDs with a high-index SiNx dielectric layer, which reduces the permittivity mismatch between the NbN wire and the surrounding area. Experimentally, a polarization sensitivity below 0.1 is obtained both at 1.31 and 1.55 µm, in excellent agreement with simulations.