We demonstrate an isolated magnetic interface anisotropy in amorphous CoFeB films on (Al)GaAs(001), similar to that in epitaxial films but without a magnetocrystalline anisotropy term. The direction of the easy axis corresponds to that due to the interfacial interaction proposed for epitaxial films. We show that the anisotropy is determined by the relative orbital component of the atomic magnetic moments. Charge transfer is ruled out as the origin of the interface anisotropy, and it is postulated that the spin-orbit interaction in the semiconductor is crucial in determining the magnetic anisotropy.