Facilitating the integration of refugees has become a major policy challenge in many host countries in the context of the global displacement crisis. One of the first policy decisions host countries make in the resettlement process is the assignment of refugees to locations within the country. We develop a mechanism to match refugees to locations in a way that takes into account their expected integration outcomes and their preferences over where to be settled. Our proposal is based on a priority mechanism that allows the government first to specify a threshold for the minimum level of expected integration success that should be achieved. Refugees are then matched to locations based on their preferences subject to meeting the government’s specified threshold. The mechanism is both strategy-proof and constrained efficient in that it always generates a matching that is not Pareto dominated by any other matching that respects the government’s threshold. We demonstrate our approach using simulations and a real-world application to refugee data from the United States.