In this paper, we study the power allocation for an integrated sensing and communication (ISAC) system which tracks a mobile target. We first model the problem as a Markov decision process, and then tackle it with a soft actor-critic (SAC) based deep reinforcement learning (DRL) approach. We also combine a Dirichlet policy, which naturally produces normalized continuous actions under random target motion. To exploit different features of sensing and communication operations, we carefully design a reward function such that the system can dynamically control power allocation to conserve resources. The simulation results demonstrate that the proposed scheme enhances tracking performance compared to other baselines while sustaining communication performance.