Using molecular simulations of nanosized aqueous droplets on a model graphite surface, we demonstrate remarkable sensitivity of water contact angles to the applied electric field polarity and direction relative to the liquid/solid interface. The effect is explained by analyzing the influence of the field on interfacial hydrogen bonding in the nanodrop, which in turn affects the interfacial tensions. The observed anisotropy in droplet wetting is a new nanoscale phenomenon that has so far been elusive as, in current experimental setups, surface molecules represent a very low fraction of the total number affected by the field. Our findings may have important implications for the design of electrowetting techniques in fabrication and property tuning of nanomaterials.