This paper emphasizes the importance of ensuring functional correctness to ensure the reliability and security of network protocol implementations, and focuses on detecting inconsistencies between RFC documents and implementations. To overcome the limitations of existing static analysis tools, we propose RFCAudit, an autonomous agent that leverages a large-scale language model (LLM) to verify the conformance between protocol implementations and RFC specifications. RFCAudit consists of an indexing agent and a detection agent. It hierarchically summarizes protocol code semantics and generates a semantic index used to narrow the scope of detection. The detection agent iteratively collects relevant data structures and functions through demand-based retrieval to effectively identify potential inconsistencies with the RFC specification. Through evaluations on six real-world network protocol implementations, RFCAudit identified 47 functional bugs with a precision of 81.9%, 20 of which were confirmed or fixed by developers.