Traffic congestion remains a significant challenge in urban management, with traditional fixed-cycle traffic signal systems struggling to adapt to dynamic traffic conditions. This paper proposes an adaptive traffic signal control method based on a Graph Neural Network (GNN) and a dynamic entropy-constrained Soft Actor–Critic (DESAC) algorithm. The approach first extracts both global and local features of the traffic network using GNN and then utilizes the DESAC algorithm to optimize traffic signal control at both single and multi-intersection levels. Finally, a simulation environment is established on the CityFlow platform to evaluate the proposed method’s performance through experiments involving single and twelve intersection scenarios. Simulation results on the CityFlow platform demonstrate that G-DESAC significantly improves traffic flow, reduces delays and queue lengths, and enhances intersection capacity compared to other algorithms. In single intersection scenarios, G-DESAC achieves a higher reward, reduced total delay time, minimized queue lengths, and improved throughput. In multi-intersection scenarios, G-DESAC maintains high rewards with stable and efficient optimization, outperforming DQN, SAC, Max-Pressure, and DDPG. This research highlights the potential of deep reinforcement learning (DRL) in urban traffic management and positions G-DESAC as a robust solution for practical traffic signal control applications, offering substantial improvements in traffic efficiency and congestion mitigation.