A sensitive apparatus utilizing a scanning Fabry-Perot interferometer excited by circularly polarized laser radiation is developed for measuring birefringence. A birefringent sample within the interferometer produces a difference in the resonance length for radiation polarized in two orthogonal directions. A Kerr cell properly oriented within the interferometer is used to cancel sample birefringence by adjusting the cell voltage. This adjustment is made by using the scanning interferometer as a spectrum analyzer and observing the displacement between the resonance curves associated with each polarization. The Kerr cell is calibrated in terms of the voltage required to produce a relative path retardation of lambda/2. The stress-induced birefringence in YAG, sapphire, and fused silica in the 26-75 degrees C temperature range is measured, and the accuracy and sensitivity of the instrument are assessed.