Integrating mobile networks with Non-3GPP networks provides a promising solution to mitigate the wireless RF spectrum scarcity. Despite the maturity of integration technologies, a comprehensive approach for radio resource allocation in highly dynamic and complex multiple Radio Access Technologies (multi-RAT) networks is still lacking. To tackle this challenge, this paper proposes an Access Traffic Management (ATM) system that enhances radio resource allocation during access, transmission, and handover processes. The system features a scalable and concise ATM-supported multi-RAT network architecture, supported by a Deep Deterministic Policy Gradient (DDPG) based Intelligent ATM (IATM) algorithm. To evaluate the proposed system, a Network Simulator 3 (NS3) based network simulation is built with realistic 5G and WiFi modules, interacting with the IATM algorithm in real time for decision making and policy improvement. Numerical improvements of our solution demonstrate its superiority over conventional steering modes. Our solution achieves an increase in resource utilization efficiency by 45\% and 70\% compared to the Active-Standby and Load-Balance steering modes, respectively. Moreover, it enhances link quality by a factor of three and doubles throughput without incurring any additional costs. Additionally, our solution significantly enhances session stability under conditions involving network size dynamics and UE mobility.