Wireless radio frequency (RF) recharging is a promising approach to prolong the lifetime of wireless sensor networks. In this paper, we describe a polling-based MAC protocol with a round robin, one-limited service policy. Upon a specific request from one or more nodes, the coordinator sends an RF recharging pulse during which regular communication is suspended. We develop a complete probabilistic model of the energy depletion process within the proposed MAC protocol as well as a queuing model of the node behavior, and use it to investigate the behavior of the time interval between successive recharging events and the packet waiting time under varying traffic load and number of nodes in the network.