Measuring the states of polarization (SoP) of light is fundamentally important for applications ranging from communication, sensing, spectroscopy, imaging, to navigation. Superconducting nanowire single-photon detectors (SNSPDs) are ideal detectors of choice for faint-light detection and measurements, but SNSPDs themselves cannot resolve the SoP of photons. Here, based on a fractal SNSPD, we demonstrate a full-Stokes polarimetric measurement system that can measure arbitrary SoP of faint light. The measured SoPs are in excellent agreement with those of a state-of-the-art commercial polarimeter, but the sensitivity of our system reaches -86.6 dBm, which is 26.6 dB better than that of the commercial counterpart. As a direct application, we further demonstrate remote polarimetric imaging (i.e., polarimetric LiDAR) with a complete set of polarimetric contrast.