In this paper, a novel birefringence measurement method through the Rayleigh backscattered lightwave within single-mode fiber is proposed, using a single chirped-pulse with arbitrary state of polarization. Numerical analysis is carried out in detail, then pulse-compression phase-sensitive optical time domain reflectometry (PC-Φ-OTDR) with polarization-diverse coherent detection is employed to verify this method. A 2 km spun single-mode fiber is tested with 8.6 cm spatial resolution, and the average birefringence of the fiber under test is measured as 0.234 rad/m, which is consistent with previous literatures about single-mode fiber. Moreover, the relationship between the measured birefringence and the spatial resolution is also studied for the first time, and the results show that spatial resolution is crucial for fiber birefringence measurement.