Conversational query rewriting is crucial for effective conversational search, yet traditional supervised methods require substantial labeled data, which is scarce in low-resource settings. This paper introduces Prompt-Guided In-Context Learning, a novel approach that leverages the in-context learning capabilities of Large Language Models (LLMs) for few-shot conversational query rewriting. Our method employs carefully designed prompts, incorporating task descriptions, input/output format specifications, and a small set of illustrative examples, to guide pre-trained LLMs to generate context-independent queries without explicit fine-tuning. Extensive experiments on benchmark datasets, TREC and Taskmaster-1, demonstrate that our approach significantly outperforms strong baselines, including supervised models and contrastive co-training methods, across various evaluation metrics such as BLEU, ROUGE-L, Success Rate, and MRR. Ablation studies confirm the importance of in-context examples, and human evaluations further validate the superior fluency, relevance, and context utilization of our generated rewrites. The results highlight the potential of prompt-guided in-context learning as an efficient and effective paradigm for low-resource conversational query rewriting, reducing the reliance on extensive labeled data and complex training procedures.