A novel technique is presented for obtaining concurrent measurements of the linear and circular birefringence properties of an optical sample by using a rotating-wave-plate Stokes polarimeter to extract the $2\times 2$ central elements of the corresponding Mueller matrix via two linearly polarized probe lights. For a compound sample comprising a half-wave plate in series with a quarter-wave plate, the measured values of the principal angle and retardance of the quarter-wave plate are found to have average normalized errors of 0.56% and 1.16%, respectively, while the measured value of the rotation angle of the half-wave plate has an error of just 0.39%. When analyzing glucose solutions with concentrations ranging from $0–1.2\mathrm{g}/\mathrm{dl}$ positioned in front of a half-wave plate, the average normalized errors in the principal axis angle and retardance measurements of the half-wave plate are 0.69% and 2.65%, respectively, while the error in the rotation angle measurements of the glucose solutions is 2.13%. The correlation coefficient between the measured rotation angle and the concentration of the glucose solution is determined to be 0.99985, while the standard deviation is just $0.0022\mathrm{deg}$ . Overall the experimental results demonstrate the ability of the proposed system to obtain highly accurate measurements of the linear and circular birefringence properties of an optical sample and to decouple the relationship between the principal axis angle and the rotation angle.