Phased array radar can simultaneously form multiple beams that can scan without inertia allowing for flexible pointing. In this paper, we propose a joint beam and dwell time allocation strategy for multi-target tracking in a phased array radar system to achieve multi-target tracking with less system resources. First, we formulate an optimization problem for minimizing the total dwell time on all targets while guaranteeing to meet a predetermined target-tracking accuracy requirement. The Bayesian Cramer-Rao Lower Bound (BCRLB) is introduced as the tracking performance metric since it provides a lower bound for the error of target state estimate. Second, after proving the optimization problem is nonconvex, we propose a two-step decomposition algorithm which is first to determine the beam pointing and then allocate the beam dwell time to solve it. Finally, we achieve multi-target tracking based on the resource allocation results. Simulation results show that our optimization strategy is effective in saving resources and is favorable for achieving a better tracking performance of worse targets as compared to an operating mode wherein uniform resource allocation occurs.