Large language model-empowered agentic recommender systems (ARS) reformulate recommendation as a multi-turn interaction between a recommender agent and a user agent, enabling iterative preference elicitation and refinement beyond conventional one-shot prediction. However, existing ARS are mainly optimized in a Reflexion-style paradigm, where past interaction trajectories are stored as textual memory and retrieved as prompt context for later reasoning. Although this design allows agents to recall prior feedback and observations, the accumulated experience remains external to model parameters, leaving agents reliant on generic reasoning rather than progressively acquiring recommendation-specific decision-making ability through learning. Reinforcement learning (RL) therefore provides a natural way to internalize such interaction experience into parameters. Yet existing RL methods for ARS still suffer from two key limitations. First, they fail to capture the interactive nature of ARS, in which the recommender agent and the user agent continuously influence each other and can naturally generate endogenous supervision through interaction feedback. Second, they reduce a rich multi-turn interaction process to final outcomes, overlooking the dense supervision embedded throughout the trajectory. To this end, we propose CoARS, a self-distilled reinforcement learning framework for co-evolving agentic recommender systems. CoARS introduces two complementary learning schemes: interaction reward, which derives coupled task-level supervision for the recommender agent and the user agent from the same interaction trajectory, and self-distilled credit assignment, which converts historical trajectories into token-level credit signals under teacher-student conditioning. Experiments on multiple datasets show that CoARS outperforms representative ARS baselines in recommendation performance and user alignment.