Opioid Use Disorder (OUD) is a chronic and relapsing condition characterized by the misuse of opioid drugs, causing significant morbidity and mortality in the United States. Existing medications for OUD are limited, and there is an immediate need to discover treatments with enhanced safety and efficacy. Drug repurposing aims to find new indications for existing medications, offering a time-saving and cost-efficient alternative strategy to traditional drug discovery. Computational approaches have been developed to further facilitate the drug repurposing process. In this paper, we reviewed state-of-the-art data-driven computational drug repurposing approaches for OUD and discussed their advantages and potential challenges. We also highlighted promising repurposed candidate drugs for OUD that were identified by computational drug repurposing techniques and reviewed studies supporting their potential mechanisms of action in treating OUD.