A sinusoidal phase-modulating Fabry-Perot interferometer is proposed. A CCD image sensor is used for measuring the distance between the transmitted beams from the two faces of the Fabry-Perot plate. From the distance, the initial angle of incidence is calculated. The sinusoidal phase-modulating interferometry is used for improving the measurement accuracy. It is insensitive to the external disturbance. Numerical calculation and experimental results make it clear that the interferometer allows high-accuracy measurements of angular displacements. The sensitivity is of the order of 10-8 rad.