We describe the unusual electro-optic response of a biaxial bent-core liquid crystal molecule that exhibits an anticlinic, antiferroelectric smectic phase (Sm-C(A)P(A)) with a molecular tilt angle close to 45°. In the ground state, the sample shows very low birefringence. A weak applied electric field distorts the antiferroelectric ground state, inducing a small azimuthal reorientation of the molecules on the tilt cone. This results in only a modest increase in the birefringence but an anomalously large (∼40°) analog rotation of the extinction direction. This unusual electro-optic response is shown to be a consequence of the molecular biaxiality.