Root Cause Analysis (RCA) plays a pivotal role in the incident diagnosis process for cloud services, requiring on-call engineers to identify the primary issues and implement corrective actions to prevent future recurrences. Improving the incident RCA process is vital for minimizing service downtime, customer impact and manual toil. Recent advances in artificial intelligence have introduced state-of-the-art Large Language Models (LLMs) like GPT-4, which have proven effective in tackling various AIOps problems, ranging from code authoring to incident management. Nonetheless, the GPT-4 model's immense size presents challenges when trying to fine-tune it on user data because of the significant GPU resource demand and the necessity for continuous model fine-tuning with the emergence of new data. To address the high cost of fine-tuning LLM, we propose an in-context learning approach for automated root causing, which eliminates the need for fine-tuning. We conduct extensive study over 100,000 production incidents, comparing several large language models using multiple metrics. The results reveal that our in-context learning approach outperforms the previous fine-tuned large language models such as GPT-3 by an average of 24.8\% across all metrics, with an impressive 49.7\% improvement over the zero-shot model. Moreover, human evaluation involving actual incident owners demonstrates its superiority over the fine-tuned model, achieving a 43.5\% improvement in correctness and an 8.7\% enhancement in readability. The impressive results demonstrate the viability of utilizing a vanilla GPT model for the RCA task, thereby avoiding the high computational and maintenance costs associated with a fine-tuned model.