A polarization-insensitive recirculating delayed self-heterodyne method (PI-RDSHM) is proposed and demonstrated for the precise measurement of sub-kilohertz laser linewidths. By a unique combination of Faraday rotator mirrors (FRMs) in an interferometer, the polarization-induced fading is effectively reduced without any active polarization control. This passive polarization-insensitive operation is theoretically analyzed and experimentally verified. Benefited from the recirculating mechanism, a series of stable beat spectra with different delay times can be measured simultaneously without changing the length of delay fiber. Based on Voigt profile fitting of high-order beat spectra, the average Lorentzian linewidth of the laser is obtained. The PI-RDSHM has advantages of polarization insensitivity, high resolution, and less statistical error, providing an effective tool for accurate measurement of sub-kilohertz laser linewidth.