High-accuracy tilt or roll angle measurement is required for a variety of engineering and scientific applications. A cyclic interferometer with multiple reflections has been developed to measure small tilt angles. To accomplish this task, a novel and simple method, phase shift by polarization, was developed. The results of these studies show that the multiple reflection cyclic interferometers can be used to measure object tilts on the order of 0.2 nano-radians. We develop the theory for polarization phase step and show that accurate measurements can be made with the cyclic interferometer.