The remarkable performance and quantum efficiency of biological light-harvesting complexes has prompted a multidisciplinary interest in engineering biologically inspired antenna systems as a possible route to novel solar cell technologies. Key to the effectiveness of biological "nanomachines" in light capture and energy transport is their highly ordered nanoscale architecture of photoactive molecules. Recently, DNA origami has emerged as a powerful tool for organizing multiple chromophores with base-pair accuracy and full geometric freedom. Here, we present a programmable antenna array on a DNA origami platform that enables the implementation of rationally designed antenna structures. We systematically analyze the light-harvesting efficiency with respect to number of donors and interdye distances of a ring-like antenna using ensemble and single-molecule fluorescence spectroscopy and detailed Förster modeling. This comprehensive study demonstrates exquisite and reliable structural control over multichromophoric geometries and points to DNA origami as highly versatile platform for testing design concepts in artificial light-harvesting networks.