Accurate medical coding requires consulting authoritative resources such as the ICD tabular list and coding guidelines. Existing LLM-based automated methods largely rely on LLMs' internal knowledge, which is prone to hallucination and cannot keep pace with guideline updates. We introduce RAG-Coding, an agentic, training-free method that augments LLMs with structured external knowledge: the tabular list is encoded as a knowledge graph capturing hierarchical and instructional code relationships, and the guidelines are distilled into concise, code-specific summaries rather than retrieved as raw text. To enable our study, we also introduce MDACE-2025, expert re-annotations of the MDACE dataset under the 2025 ICD-10-CM/PCS guidelines, adding code sequencing and justification comments. On MDACE, RAG-Coding outperforms the best LLM-based baseline by 3--13\% in micro-F1 across five LLM backbones, and achieves comparable micro- and macro-F1 to the supervised state-of-the-art, with higher recall ($+$11\%) at the cost of precision ($-$6\%). On MDACE-2025, RAG-Coding outperforms all baselines, demonstrating effective generalisation to updated guidelines. Ablations confirm stepwise gains, highlighting the importance of integrating structured external knowledge for LLM-based medical coding.