Considering that delay/disruption-tolerant networks (DTNs) suffer from a large variation of network topology, geographic routing is an alternative scheme that utilizes real-time geographic information instead of network topology information. However, the real-time geographic information of mobile destination is likely unavailable due to sparse network density. With this in mind, we propose a geographic routing scheme by relying on historical geographic information to estimate the movement range of destination. The idea is to make efficient message replication toward this estimated range via the proposed Approach Phase to reduce routing overhead. Meanwhile, the effective message replication within this range is guaranteed via the proposed Roam Phase to increase the message delivery ratio. We further propose a novel scheme to handle the local maximum problem for geographic routing in sparse networks. Simulation results obtained assuming the maps of three real world cities, namely, Helsinki, Finland; Karlsruhe, Germany; and Manhattan, New York City, USA, show an advantage of the proposed Approach-and-Roam (AaR) over the compared algorithms in terms of delivery ratio, average delivery latency, and overhead ratio.