Reconfigurable Intelligent Surfaces (RIS) represent a breakthrough in wireless communication, enhancing signal quality and network coverage through intelligent wave manipulation. However, traditional RIS systems face challenges in dynamic environments and high-latency scenarios. This study introduces a novel Cache-at-RIS framework, integrating caching capabilities with a Transformer-based predictive caching mechanism. The Transformer model leverages its self-attention mechanism to analyze user request patterns, accurately predicting future demands and optimizing cache management. By dynamically adjusting RIS parameters and preloading frequently requested data, the framework significantly reduces latency and improves achievable rates, particularly in high-frequency bands and dense user environments. Key findings demonstrate the superiority of Cache-at-RIS in supporting ultra-low latency applications, such as AR/VR and autonomous driving, while also reducing energy consumption. This work advances the integration of intelligent communication and edge computing, offering a scalable and efficient solution for next-generation 6G networks.