As an approach for electrically controllable actuators, we prepare elastomers of chiral smectic-A liquid crystals, which have an electroclinic effect, i.e., molecular tilt induced by an applied electric field. Surprisingly, our experiments find that an electric field causes a rapid and reversible twisting of the film out of the plane, with a helical sense that depends on the sign of the field. To explain this twist, we develop a continuum elastic theory based on an asymmetry between the front and back of the film. We further present finite-element simulations, which show the dynamic shape change.