SchedCP is the first framework to leverage Large Language Model (LLM) agents to optimize the performance of operating system schedulers. To address the fundamental problem of existing schedulers' lack of understanding of application-specific requirements, we propose a decoupled control plane architecture that separates AI's semantic reasoning (what to optimize) from system execution (how to observe and act). Implemented as a Model Context Protocol (MCP) server, SchedCP provides three main services: a workload analysis engine, an evolving scheduler policy repository, and an execution verifier that verifies AI-generated code and configurations through static and dynamic analysis. A multi-agent system called sched-agent autonomously analyzes workloads, synthesizes customized eBPF scheduling policies, and deploys them via the sched_ext infrastructure. Evaluation results show that SchedCP achieves up to 1.79x performance gains and 13x cost reductions compared to existing approaches, while maintaining a high success rate. This enables expert-level system optimization and represents a step toward a self-optimizing, application-aware operating system.