Magnetic anisotropy (MA) is one of the most important material properties for modern spintronic devices. Conventional manipulation of the intrinsic MA, i.e., magnetocrystalline anisotropy (MCA), typically depends upon crystal symmetry. Extrinsic control over the MA is usually achieved by introducing shape anisotropy or exchange bias from another magnetically ordered material. Here we demonstrate a pathway to manipulate MA of 3d transition-metal oxides (TMOs) by digitally inserting nonmagnetic 5d TMOs with pronounced spin-orbit coupling (SOC). High-quality superlattices comprising ferromagnetic La2/3Sr1/3MnO3 (LSMO) and paramagnetic SrIrO3 (SIO) are synthesized with the precise control of thickness at the atomic scale. Magnetic easy-axis reorientation is observed by controlling the dimensionality of SIO, mediated through the emergence of a novel spin-orbit state within the nominally paramagnetic SIO.