Magnetoelectric response in thin films is highly desirable for high-throughput and high-density microelectronic applications, like magnetic sensors. To sensitively detect the direction of magnetic field, the anisotropic magnetoelectric effect is required. Here, we artificially design an anisotropic magnetoelectric response in Sr2IrO4/SrTiO3 superlattices, where a strong (negligible) magnetoelectric response for magnetic fields along the z-direction (xy-plane) of Sr2IrO4/SrTiO3 interface was observed. A combination of perturbative calculations with numerical results and density functional theory calculations reveals that only the effective z-component Zeeman field within the Sr2IrO4 layers can change the electron occupation of the neighboring SrTiO3 layers, which is proportional to the polarization. Via controlling the periodicity of the superlattices, we can further control the anisotropy of magnetoelectric responses. This atomic-scale design of 3d/5d superlattices paves an alternative way toward controllable magnetoelectric effects with thin film integrations.