Superconducting nanowire single photon detectors (SNSPDs) have been extensively investigated due to their superior characteristics, including high system detection efficiency, low dark count rate and short recovery time. The polarization sensitivity introduced by the meandering-type superconductor nanowires is an intrinsic property of SNSPD, which is normally measured by sweeping hundreds of points on the Poincaré sphere to overcome the unknown birefringent problem of the SNSPD's delivery fiber. In this paper, we propose an alternative method to characterize the optical absorptance of SNSPDs, without sweeping hundreds of points on the Poincaré sphere. It is shown theoretically that measurements on the system detection efficiencies (SDEs) subject to cases of four specific photon polarization states are sufficient to reveal the two eigen-absorptances of the SNSPD. We validate the proposed method by comparing the measured detection spectra with the spectra attained from sweeping points on the Poincaré sphere and the simulated absorption spectra.