To efficiently archive and query data in wireless sensor networks (WSNs), distributed storage systems, and multisink schemes have been proposed recently. However, such distributed access cannot be fully supported and exploited by existing routing protocols in a large-scale WSN. In this paper, we will address this challenging issue and propose a distributed geographic K-anycast routing (GKAR) protocol for WSNs, which can efficiently route data from a source sensor to any K destinations (e.g., storage nodes or sinks). To guarantee K-delivery, an iterative approach is adopted in GKAR where in each round, GKAR will determine not only the next hops at each node, but also a set of potential destinations for every next hop node to reach. Efficient algorithms are designed to determine the selection of the next hops and destination set division at each intermediate node. We analyze the complexity of GKAR in each round and we also theoretically analyze the expected number of rounds required to guarantee K-delivery. Simulation results demonstrate the superiority of the GKAP scheme in reducing the total duration and the communication overhead for finding K destinations, by comparing with the existing schemes, e.g., K 1-anycast .