Ensuring the reliability and availability of cloud services necessitates efficient root cause analysis (RCA) for cloud incidents. Traditional RCA methods, which rely on manual investigations of data sources such as logs and traces, are often laborious, error-prone, and challenging for on-call engineers. In this paper, we introduce RCACopilot, an innovative on-call system empowered by the large language model for automating RCA of cloud incidents. RCACopilot matches incoming incidents to corresponding incident handlers based on their alert types, aggregates the critical runtime diagnostic information, predicts the incident's root cause category, and provides an explanatory narrative. We evaluate RCACopilot using a real-world dataset consisting of a year's worth of incidents from Microsoft. Our evaluation demonstrates that RCACopilot achieves RCA accuracy up to 0.766. Furthermore, the diagnostic information collection component of RCACopilot has been successfully in use at Microsoft for over four years.