Linux kernel tuning is essential for optimizing operating system (OS) performance, yet remains challenging due to the complex kernel space, sparse performance feedback, and strong workload sensitivity. We present TuneAgent, an agentic Linux kernel tuning framework powered by rule-based reinforcement learning (RL). TuneAgent formulates the kernel space as a constrained RL environment, enabling large language models (LLMs) to autonomously explore the kernel while enforcing valid and precise configuration modifications. To address sparse performance feedback, we design structured reward functions that jointly promote reasoning standardization, configuration correctness, and performance awareness. Furthermore, we propose a two-phase training strategy that first ensures format and semantic correctness and then transitions to performance-driven exploration, accelerating convergence and reducing overhead. Experimental results show that TuneAgent consistently outperforms existing baselines, achieving up to 5.6% relative overall performance improvement while maintaining high configuration validity. We further demonstrate its robustness across multiple real-world applications, highlighting its practicality and adaptability in diverse deployment environments.