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The rapid development of Network Function Virtualization (NFV) enables network operators to deliver customized end-to-end services through Service Function Chains (SFCs). However, existing two-stage deployment strategies fail to jointly optimize the placement of Virtual Network Functions (VNFs) and the routing of service traffic, resulting in inefficient resource utilization and increased service latency. This study addresses the challenge of maximizing the acceptance rate of service requests under resource constraints and latency requirements. We propose DRL-FJM, a novel dynamic SFC joint mapping orchestration algorithm based on Deep Reinforcement Learning (DRL). By holistically evaluating network resource states, the algorithm jointly optimizes node and link mapping schemes to effectively tackle the dual challenges of resource limitations and latency constraints in long-term SFC orchestration scenarios. Simulation results demonstrate that compared with existing methods, DRL-FJM improves total traffic served by up to 42.6%, node resource utilization by 17.3%, and link resource utilization by 26.6%, while achieving nearly 100% SFC deployment success. Moreover, our analysis reveals that the proposed algorithm demonstrates strong adaptability and robustness under diverse network conditions.