The increasing complexity of integrated circuits (ICs) poses significant challenges for Electronic Design Automation (EDA) tools, particularly for novice users. Debugging EDA issues can be time-consuming and frustrating due to complex error messages, extensive documentation, and limited knowledge sharing. While open-source EDA tools like OpenROAD and OpenLane have democratized chip design, the reliance on expert knowledge and the long response times for issue resolution remain significant obstacles. To address these challenges, we introduce EDA-Debugger, a novel multi-agent LLM-based framework for automated EDA issue resolution. EDA-Debugger leverages the power of LLMs to analyze EDA log files, identify potential issues, and provide actionable solutions. By integrating domain-specific Retrieval Augmented Generation (RAG), EDA-Debugger bridges the gap between designers, LLMs, and EDA tools, enhancing efficiency, accuracy, and accessibility for users of all skill levels. Our evaluation of a benchmark dataset of 20 typical Open EDA issues not in the dataset, shows a \textit{50\%} improvement on issue resolution and \textit{20.1\%} improvement on average score compared to using GPT-4 alone. This paper outlines the architecture, functionalities, and evaluation of EDA-Debugger, demonstrating its potential to revolutionize the EDA debugging process.