Cooperative Adaptive Cruise Control (CACC) represents a quintessential control strategy for orchestrating vehicular platoon movement within Connected and Automated Vehicle (CAV) systems, significantly enhancing traffic efficiency and reducing energy consumption. In recent years, the data-driven methods, such as reinforcement learning (RL), have been employed to address this task due to their significant advantages in terms of efficiency and flexibility. However, the delay issue, which often arises in real-world CACC systems, is rarely taken into account by current RL-based approaches. To tackle this problem, we propose a Delay-Aware Multi-Agent Reinforcement Learning (DAMARL) framework aimed at achieving safe and stable control for CACC. We model the entire decision-making process using a Multi-Agent Delay-Aware Markov Decision Process (MADA-MDP) and develop a centralized training with decentralized execution (CTDE) MARL framework for distributed control of CACC platoons. An attention mechanism-integrated policy network is introduced to enhance the performance of CAV communication and decision-making. Additionally, a velocity optimization model-based action filter is incorporated to further ensure the stability of the platoon. Experimental results across various delay conditions and platoon sizes demonstrate that our approach consistently outperforms baseline methods in terms of platoon safety, stability and overall performance.