To provide various high-quality intelligent transportation services to customers, Intelligent Cyber-Physical Transportation Systems (ICTS) with cloud-edge computing are widely commissioned. In such ICTS, service requests processed by edge servers (ES) usually have a low response latency, thus leading to a high quality of service (QoS). As a prerequisite for requests processing in the ES, service cache provides requests with storage and computing resources. But the limited resources of each ES make it impossible to cache all services, so how to generate high-performance caching strategies for ICTS is a major challenge. Besides, how to evaluate the effectiveness of the application of these strategies is also a challenge. Fortunately, thanks to the constructed digital twins (DT) for ICTS, the strategies have a digital platform to be simulated into application. With the assistance of DT, a solution to service caching problem in ICTS, named SFT-SCAR, is proposed. Firstly, a DT supported service providing framework for ICTS is designed. Then, a graph attention network (GAT) based service request flow prediction scheme and an asynchronous advantage actor-critic (A3C) based service caching scheme are presented. Besides, the generated caching strategies are simulated in the DT of ICTS to evaluate the performance of these strategies. Experimental results demonstrate that the proposed SFT-SCAR approach improves the hit rate by 1.11% - 13.27%.