A linear electrogyration effect has been identified in crystalline $\alpha $-quartz. This is an effect whereby the polarization direction of a linearly polarized light wave propagating in the crystal is rotated by the application of a transverse electric field. It is thus an electric field dependence of the optical activity in quartz. The third rank tensor characterizing the effect has been fully quantified. The effect has potential usefulness in measurement transducers and in optical modulators.