Biomedical Terminology Normalization aims to identify the standard term in a specified termbase for non-standardized mentions from social media or clinical texts, employing the mainstream “Recall and Re-rank” framework. Instead of the traditional pretraining-finetuning paradigm, we would like to explore the possibility of accomplishing this task through a tuning-free paradigm using powerful Large Language Models (LLMs), hoping to address the costs of re-training due to discrepancies of both standard termbases and annotation protocols. Another major obstacle in this task is that both mentions and terms are short texts. Short texts contain an insufficient amount of information that can introduce ambiguity, especially in a biomedical context. Therefore, besides using the advanced embedding model, we implement a Retrieval-Augmented Generation (RAG) based knowledge card generation module. This module introduces an LLM agent that expands the short texts into accurate, harmonized, and more informative descriptions using a search engine and a domain knowledge base. Furthermore, we present an innovative tuning-free agent collaboration framework for the biomedical terminology normalization task in social media. By leveraging the internal knowledge and the reasoning capabilities of LLM, our framework conducts more sophisticated recall, ranking and re-ranking processes with the collaboration of different LLM agents. Experimental results across multiple datasets indicate that our approach exhibits competitive performance. We release our code and data on the github repository JOHNNY-fans/RankNorm.