With the rapid growth of the mobility-on-demand (MoD) market in recent years, ride-hailing companies have become an important element of the urban mobility system. There are two critical components in the operations of ride-hailing companies: driver-customer matching and vehicle rebalancing. In most previous literature, each component is considered separately, and performances of vehicle rebalancing models rely on the accuracy of future demand predictions. To better immunize rebalancing decisions against demand uncertainty, a novel approach, the matching-integrated vehicle rebalancing (MIVR) model, is proposed in this paper to incorporate driver-customer matching into vehicle rebalancing problems to produce better rebalancing strategies. The MIVR model treats the driver-customer matching component at an aggregate level and minimizes a generalized cost including the total vehicle miles traveled (VMT) and the number of unsatisfied requests. For further protection against uncertainty, robust optimization (RO) techniques are introduced to construct a robust version of the MIVR model. Problem-specific uncertainty sets are designed for the robust MIVR model. The proposed MIVR model is tested against two benchmark vehicle rebalancing models using real ride-hailing demand and travel time data from New York City (NYC). The MIVR model is shown to have better performances by reducing customer wait times compared to benchmark models under most scenarios. In addition, the robust MIVR model produces better solutions by planning for demand uncertainty compared to the non-robust (nominal) MIVR model.