Reasoning capabilities are crucial for reliable medical visual question answering (VQA); however, existing datasets rarely include reasoning explanations. We address this by generating reasoning trajectories for six medical VQA benchmarks using the COMCTS algorithm with open-source vision-language models, with an LLM serving as the verification judge. Building on these generated datasets, we propose a two-stage training framework: supervised fine-tuning followed by Group Relative Policy Optimization (GRPO) with a novel process-based reward. While standard approaches rely solely on exact-match rewards for final answers, we introduce a trajectory-aware reward that measures the similarity between generated and ground-truth reasoning processes. Specifically, we embed reasoning steps using sentence transformers and compute the Dynamic Time Warping (DTW) distance between the resulting vector sequences. Experiments across six benchmarks demonstrate that combining the DTW-based process reward with exact-match reward consistently outperforms SFT-only training, raising mean accuracy from 0.598 to 0.689, mean BERTScore from 0.845 to 0.881, and mean ROUGE-L from 0.665 to 0.748. Our results highlight the importance of process supervision in training reasoning-capable medical VLMs. We make our code and generated reasoning datasets publicly available at https://anonymous.4open.science/r/MICCAI-R1-MED-VQA-code-B14B/