Magnetoelectric coupling is studied using the electric field between the tip of a spin-polarized scanning tunneling microscope and a nanomagnet. Our experiments show that a negative (positive) electric field stabilizes (destabilizes) in-plane magnetization against thermal agitation, whereas it destabilizes (stabilizes) out-of-plane magnetization. We conclude that the electric field E induces a uniaxial anisotropy that favors in-plane magnetization for E < 0 and out-of-plane magnetization for E > 0. Our experiments demonstrate magnetic manipulation on the atomic scale without exploiting spin or charge currents.