Communication topology is a crucial part of a distributed control implementation for cyber-physical systems, yet is typically treated as a constraint within control design problems rather than a design variable. We propose a data-driven method for designing an optimal topology for the purpose of distributed control when a system model is unavailable or unaffordable, via a mixed-integer second-order conic program. The approach demonstrates improved control performance over random topologies in simulations and efficiently drops links which have a small effect on predictor accuracy, which we show correlates well with closed-loop control cost.