Automatic Speech Recognition (ASR) systems have demonstrated remarkable performance across various applications. However, limited data and the unique language features of specific domains, such as low-resource languages, significantly degrade their performance and lead to higher Word Error Rates (WER). In this study, we propose Generative Error Correction via Retrieval-Augmented Generation (GEC-RAG), a novel approach designed to improve ASR accuracy for low-resource domains, like Persian. Our approach treats the ASR system as a black-box, a common practice in cloud-based services, and proposes a Retrieval-Augmented Generation (RAG) approach within the In-Context Learning (ICL) scheme to enhance the quality of ASR predictions. By constructing a knowledge base that pairs ASR predictions (1-best and 5-best hypotheses) with their corresponding ground truths, GEC-RAG retrieves lexically similar examples to the ASR transcription using the Term Frequency-Inverse Document Frequency (TF-IDF) measure. This process provides relevant error patterns of the system alongside the ASR transcription to the Generative Large Language Model (LLM), enabling targeted corrections. Our results demonstrate that this strategy significantly reduces WER in Persian and highlights a potential for domain adaptation and low-resource scenarios. This research underscores the effectiveness of using RAG in enhancing ASR systems without requiring direct model modification or fine-tuning, making it adaptable to any domain by simply updating the transcription knowledge base with domain-specific data.