We propose a modulation-free technique for frequency stabilization of an external-cavity diode laser (ECDL) by using a phase-difference biased Sagnac interferometer to produce dispersion spectroscopic error signals. A half-wave plate and a total internal reflection prism are inserted into the loop to provide a phase-difference bias between the clockwise and counterclockwise beams with perpendicular polarizations, instead of the previous method with misaligned optical paths. In the experiments, the frequency of the Littman-Metcalf configuration ECDL is locked at the transition of the Rb atomic vapor, and the frequency fluctuation is suppressed from 8 to less than 0.5 MHz peak to peak. It is shown that this scheme is simple, robust, low cost, and it shows promise for use in a variety of related applications.