Biomedical ontologies, which comprehensively define concepts and relations for biomedical entities, are crucial for structuring and formalizing domain-specific information representations. Biomedical code mapping identifies similarity or equivalence between concepts from different ontologies. Obtaining high-quality mapping usually relies on automatic generation of unrefined mapping with ontology domain fine-tuned language models (LMs), followed by manual selections or corrections by coding experts who have extensive domain expertise and familiarity with ontology schemas. The LMs usually provide unrefined code mapping suggestions as a list of candidates without reasoning or supporting evidence, hence coding experts still need to verify each suggested candidate against ontology sources to pick the best matches. This is also a recurring task as ontology sources are updated regularly to incorporate new research findings. Consequently, the need of regular LM retraining and manual refinement make code mapping time-consuming and labour intensive. In this work, we created OntologyRAG, an ontology-enhanced retrieval-augmented generation (RAG) method that leverages the inductive biases from ontological knowledge graphs for in-context-learning (ICL) in large language models (LLMs). Our solution grounds LLMs to knowledge graphs with unrefined mappings between ontologies and processes questions by generating an interpretable set of results that include prediction rational with mapping proximity assessment. Our solution doesn't require re-training LMs, as all ontology updates could be reflected by updating the knowledge graphs with a standard process. Evaluation results on a self-curated gold dataset show promises of using our method to enable coding experts to achieve better and faster code mapping. The code is available at https://github.com/iqvianlp/ontologyRAG.