Low-altitude Communication Network (LCN) refers to network systems that employ drones and other low-altitude aerial platforms as carriers. Leveraging advanced communication technologies and data processing methodologies, these networks enable high-efficiency data transmission in low-altitude airspace, thus emerging as a pivotal driver for the advancement of the low-altitude economy. With the continuous advancement of Unmanned Aerial Vehicle (UAV), artificial intelligence, and communication technologies, LCN have been increasingly integrated into smart city construction, Internet of Things expansion, emergency management, and other fields. As a core component of these sectors, LCN have effectively driven the robust development of the low-altitude economy. Within the context of LCN, the efficient deployment of Service Function Chain (SFC) emerges as a critical factor in optimizing network service capabilities and enhancing resource utilization efficiency. In the dynamic and complex operating environment of LCN, reasonable and efficient SFC deployment can effectively coordinate the allocation of communication, computing, and storage resources, laying a solid foundation for the stable and high-quality operation of various network services. However, existing deployment algorithms either fail to fully consider the dynamic changes in the LCN or lack sufficient exploratory strategies, making them difficult to adapt to the diverse business scenarios within the LCN. To address the issue, our study proposes a dynamic SFC deployment method based on the Asynchronous Advantage Actor-Critic (A3C) and Graph Attention Network (GAT) algorithms. The experimental findings indicate that our proposed algorithm achieves a notable reduction in orchestration expenses, while simultaneously enhancing resource utilization, thus exhibiting excellent performance and robust adaptability in dynamic LCN environments.