We present a new method for quantification of minute birefringence in high-finesse resonators. The method is based on observing the homodyne polarization mode beat at the output of the resonator. We show that the mode beat is generated by a phase mismatch of a polarization mode in the cavity and that the magnitude of the birefringence is proportional to the beat frequency. We demonstrate the sensitivity of the technique by measuring polarization properties of a twisted 0.275 m long single-mode fiber cavity. Maximum beat length of the fiber was found to be 10.6 m, which is almost 40 times longer than the length of the studied fiber.