Recent advancements in Large Language Models (LLMs) have notably enhanced task-oriented dialogue systems, particularly in Dialogue State Tracking (DST), owing to their generative capabilities and strong generalization. Although recent approaches such as LDST and FnCTOD significantly improved cross-domain DST performance via supervised fine-tuning (SFT), these methods typically require substantial amounts of domain-specific data. In this paper, we address this limitation by employing Group Relative Policy Optimization (GRPO) - a critic-free reinforcement learning method that efficiently guides LLMs toward improved DST accuracy even under low-resource conditions. Our results on established DST benchmarks, including MultiWOZ 2.1 and 2.4, demonstrate that the RL approach achieves superior performance to existing methods while using significantly reduced out-of-domain training data. In addition, we found out that models pretrained specifically for tool-use tasks can be a better starting point, especially on small scales.