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Modern short-range gravity experiments that seek to test the Newtonian inverse-square law or weak equivalence principle of general relativity typically involve measuring the minute variations in the twist angle of a torsion pendulum. Motivated by various theoretical arguments, recent efforts largely focus on measurements with test mass separations in the sub-millimeter regime. To measure the twist, many experiments employ an optical autocollimator with a noise performance of ∼300 nrad[Formula: see text] in the 0.1–10 mHz band, enabling a measurement uncertainty of a few nanoradians in a typical integration time. We investigated an alternative method for measuring a small twist angle through the construction of a modified Michelson interferometer. The main modification is the introduction of two additional arms that allow for improved angular alignment. A series of detectors and LabView software routines were developed to determine the orientation of a mirror attached to a sinusoidally driven rotation stage that oscillated with an amplitude of 0.35 mrad and a period of 200 s. In these measurements, the resolution of the interferometer is 8.1  μrad per fringe, while its dynamic range spanned 0.962 mrad. We compare the performance of this interferometric optical system to existing autocollimator-based methods, discussing its implementation, possible advantages, and future potential, as well as disadvantages and limitations.