The theory of ab initio semi-relativistic angle-resolved photoemission calculations is formulated within the real-space multiple-scattering theory and the single-particle approximation. It has the flexibility and simplicity required for studying systems with layered structures and more general complex geometries. For layered structures the layer-resolved potentials are obtained self-consistently using the Korringa-Kohn-Rostoker (KKR) method. The advantage of the present approach is that the self-consistent potential and the photocurrent are treated on the same footing and calculated within the same formalism. The approach is illustrated through a study of the angle-resolved photoemission for real-space, layered systems with two-dimensional periodicity, with specific application to Cu.