Although centrality is widely used to differentiate the importance of nodes for social-aware routing in mobile opportunistic networks (MONs), it is destination-agnostic since such metrics are usually measured without destination information. To this end, we propose a destination-aware social routing scheme for MONs, namely DAS, which utilizes the destination-aware betweenness centrality (DBC) to choose the right nodes as relays given the specific destination node. During the process of message dissemination, the number of replicas for a message is calculated by the source and each relay independently in respond to the network condition in a dynamic manner. Therefore, DAS disseminates only a few message copies to ensure data delivery as well as reducing routing cost. We conduct extensive simulations using real trace data sets to show improved performance with low overhead in comparison with existing social-aware routing approaches in various scenarios.