Common Data Elements (CDEs) standardize data collection and sharing across studies, enhancing data interoperability and improving research reproducibility. However, implementing CDEs presents challenges due to the broad range and variety of data elements. This study aims to develop an effective and efficient mapping tool to bridge the gap between local data elements and National Institutes of Health (NIH) CDEs. We propose CDEMapper, a large language model (LLM) powered mapping tool designed to assist in mapping local data elements to NIH CDEs. CDEMapper has three core modules: (1) CDE indexing and embeddings. NIH CDEs were indexed and embedded to support semantic search; (2) CDE recommendations. The tool combines Elasticsearch (BM25 similarity methods) with state of the art GPT services to recommend candidate CDEs and their permissible values; and (3) Human review. Users review and select the NIH CDEs and values that best match their data elements and value sets. We evaluate the tool recommendation accuracy against manually annotated mapping results. CDEMapper offers a publicly available, LLM-powered, and intuitive user interface that consolidates essential and advanced mapping services into a streamlined pipeline. It provides a step by step, quality assured mapping workflow designed with a user-centered approach. The evaluation results demonstrated that augmenting BM25 with GPT embeddings and a ranker consistently enhances CDEMapper mapping accuracy in three different mapping settings across four evaluation datasets. This work opens up the potential of using LLMs to assist with CDE recommendation and human curation when aligning local data elements with NIH CDEs. Additionally, this effort enhances clinical research data interoperability and helps researchers better understand the gaps between local data elements and NIH CDEs.