We propose a scalable analog quantum simulator for quantum electrodynamics (QED) in two spatial dimensions. The setup for the U(1) lattice gauge field theory employs inter-species spin-changing collisions in an ultra-cold atomic mixture trapped in an optical lattice. Building on the previous one-dimensional implementation scheme of Ref.  we engineer spatial plaquette terms for magnetic fields, thus solving a major obstacle towards experimental realizations of realistic gauge theories in higher dimensions. We apply our approach to pure gauge theory and discuss how the phenomenon of confinement of electric charges can be described by the quantum simulator.