Recent advances in large language models (LLMs) have demonstrated impressive capabilities in code-related tasks, such as code generation and automated program repair. Despite their promising performance, most existing approaches for code repair suffer from high training costs or computationally expensive inference. Retrieval-augmented generation (RAG), with its efficient in-context learning paradigm, offers a more scalable alternative. However, conventional retrieval strategies, which are often based on holistic code-text embeddings, fail to capture the structural intricacies of code, resulting in suboptimal retrieval quality. To address the above limitations, we propose ReCode, a fine-grained retrieval-augmented in-context learning framework designed for accurate and efficient code repair. Specifically, ReCode introduces two key innovations: (1) an algorithm-aware retrieval strategy that narrows the search space using preliminary algorithm type predictions; and (2) a modular dual-encoder architecture that separately processes code and textual inputs, enabling fine-grained semantic matching between input and retrieved contexts. Furthermore, we propose RACodeBench, a new benchmark constructed from real-world user-submitted buggy code, which addresses the limitations of synthetic benchmarks and supports realistic evaluation. Experimental results on RACodeBench and competitive programming datasets demonstrate that ReCode achieves higher repair accuracy with significantly reduced inference cost, highlighting its practical value for real-world code repair scenarios.