A simple polarized-light-based phase shifting method for analyzing fringe patterns formed in Burch's common-path scatterplate interferometer is proposed. The system employs circularly polarized beam at the input, a small quarter-wave plate acting on the reference beam only, and a rotating analyzer in two orthogonal circular polarization beams at the output of the interferometer. The simplicity of our approach is proved theoretically and experimentally. Problems related to nonideal light modulation at the output and the ways to overcome them are discussed.