A finite degree of in-plane twist is predicted to produce a surface polar electro-optic (EO) effect in nematic liquid crystals (NLCs). It is found that the flexoelectric coupling with an external electric field essentially renormalizes anchoring energies at the solid-NLC interfaces. Because of the anchoring renormalization by out-of-plane tilt and/or in-plane twist the symmetry of the system is broken, and the polar EO effect is thus induced. The EO modulation exhibits a peak near the Fredericks transition, which agrees well with numerical simulations.