This paper presents a risk assessment framework for integrating artificial intelligence (AI) into cybersecurity strategies, utilizing a hybrid approach that combines ISO 31000 and FMEA methodologies. The framework systematically evaluates risks at each stage of AI integration, from security needs analysis to ongoing monitoring. Key risks identified include incomplete security needs, inappropriate AI technology selection, and poor-quality training data. Mitigation strategies, such as thorough needs analysis and regular bias audits, are outlined to address these risks. The approach optimizes resources and enhances security, although its effectiveness may vary based on existing controls. This study emphasizes the importance of continuous monitoring and adaptation, providing practical insights for organizations aiming to improve cybersecurity through AI.