An angular and displacement sensor that uses a polymer optical fiber and Moiré patterns is demonstrated. Moiré fringes are generated using two transparent superimposed planar gratings placed in front of an optical mirror. Moiré patterns with periods ranging from 0.4 to 2 mm have been obtained in this way with lmm-diameter plastic optical fibers for torsion angles ranging from 10° to 20° have been compared with theoretical calculations and a good agreement has been confirmed. Measuring the period length and the number of periods, both the relative angle between the gratings and the displacement of the fiber with respect to the mirror are obtained. With this technique very low angles can be measured with a very high resolution. The sensor principle has been successfully checked in the laboratory. Finally, the effect of employing different plastic fibers is also discussed. Besides, other possible applications of this measurement technique are presented and discussed.