We demonstrate a two-dimensional 11-zone ion trap array, where individual laser-cooled atomic ions are stored, separated, shuttled, and swapped. The trap geometry consists of two linear rf ion trap sections that are joined at a 90 degree angle to form a T-shaped structure. We shuttle a single ion around the corners of the T-junction and swap the positions of two crystallized ions using voltage sequences designed to accommodate the nontrivial electrical potential near the junction. Full two-dimensional control of multiple ions demonstrated in this system may be crucial for the realization of scalable ion trap quantum computation and the implementation of quantum networks.