Ultrathin Fe films were grown epitaxially onto a stepped W(001) substrate, polished with a curvature to provide a continuously variable step density, with the steps parallel to the [100] crystalline axis. The steps induce an in-plane uniaxial magnetic anisotropy with easy axis perpendicular to the step edges. We found that this step-induced magnetic anisotropy does not enhance the Curie temperature of the Fe film. The strength of the anisotropy varies quadratically with step density, but does not decay with 1/d dependence expected for a surface-type anisotropy. We suggest that strain at the step edges might underlie the result.