We developed an efficient method for measuring the principal refractive indices and thickness of an optically anisotropic wafer that involves the analysis of Fabry-Perot interference fringes. Utilizing the birefringence of the medium, the 2π phase ambiguity was readily resolved in single-wavelength measurements of the birefringent medium index. Although the accuracy of the index measurements is limited due to the innate ambiguity, our analysis method overcame this limit and could determine the principal refractive indices and thickness with an uncertainty of 10(-5). Our method was validated against measurements of a lithium niobate wafer for which the values of the indices are precisely known.