Conversational stance detection requires identifying the stance of a current utterance toward a target within its dialogue context. Existing methods often rely on sequential encoding, fixed knowledge-integration pipelines, or uniform reasoning strategies, which limits their ability to capture cross-turn dependencies and adapt to instance-specific needs. We propose StanceAgent-R1, an agentic reinforcement learning framework that adaptively routes each instance to evidence-path selection and/or knowledge elicitation. The model is first warm-started with rejection-sampled expert trajectories and then optimized with a progressive trajectory-faithful reward that encourages correct, well-formed, and route-consistent reasoning. Experiments on ZS-CSD, MT-CSD, and C-MTCSD show that StanceAgent-R1 achieves state-of-the-art performance, with further analyses confirming the effectiveness of its agentic design and reward strategy.