Designing efficient routing protocols for a wireless sensor network with mobile sinks (mWSN) is a challenging task since the network topology and data paths change frequently as sink nodes move. In this paper, we design a novel lightweight reactive ring based routing protocol called R3, which removes the need of proactively maintaining data paths to mobile sinks as they move in the network. To achieve high packet delivery ratio and low transmission cost, R3 combines ring based forwarding and trail based forwarding together. To support efficient ring based forwarding, we build a ring based structure for a network in a way such that each node in the network can easily obtain its ring ID and virtual angle information. For this purpose, we artificially create a virtual hole in the central area of the network and accordingly find a shortest cycled path enclosing the hole, which serves as base ring and is used for generating the remaining ring based structure. We accordingly present the detailed design description for R3, which only requires each node to keep very limited routing information. We derive the communication overhead by ring based forwarding. Extensive simulation results show that R3 can achieve high routing performance as compared with existing work.