One path to realizing systems of trapped atomic ions suitable for large-scale quantum computing and simulation is to create a two-dimensional array of ion traps. Interactions between nearest-neighbouring ions could then be turned on and off by tuning the ions relative positions and frequencies. We demonstrate and characterize the operation of a planar-electrode ion-trap array. Driving the trap with a network of phase-locked radio-frequency (RF) resonators which provide independently variable voltage amplitudes we vary the position and motional frequency of a 40Ca+ ion in two dimensions within the trap array. With suitable miniaturization of the trap structure, this provides a viable architecture for large-scale quantum simulations.