We demonstrate the localization of quantum-well excitons in a periodic array of linear traps using photoluminescence experiments. The excitonic traps are induced by applying spatially alternating external voltages via interdigitated metal gates. The localization originates from the periodical modulation of the strength of the quantum-confined Stark effect in the plane of the quantum well. In our experiments, the trap depth is easily tuned by the voltages applied to the interdigitated gates. Furthermore, we find that a perpendicular magnetic field reduces the exciton diffusion length. In short-period lateral superlattices, we observe a magnetic-field-induced stabilization of excitons in the presence of strong in-plane electric fields.