Mobile edge computing (MEC) provides a novel computing paradigm to satisfy the increasing computation requirements of mobile applications. In MEC-enabled intelligent transportation systems (ITS), the latency-sensitive computing tasks are offloaded to RSUs for execution, reducing the transmission latency compared with the cloud solutions. However, the repetitive executions of the same tasks whose outputs are dependent on the inputs lead to the extra system latency, an alternative is to cache the required services on RSUs in advance. The service requirements of latency-sensitive computing tasks are satisfied by jointly considering computation offloading and service caching. Besides, the digital twin (DT) is utilized to construct the virtual world reflecting the physical world in real-time to efficiently make offloading strategies. In this paper, a computation offloading and service caching method using decision theory in ITS with DT, named CODT, is proposed. Specifically, the computation offloading and service caching in ITS is modeled first with DT. Then, a mixed-integer nonlinear programming (MINLP) problem is formulated to minimize the system latency. Afterward, the decision theory is used to analyze the utilities of offloading strategies in different states of RSUs and make the optimal strategy. Finally, extensive simulations based on the real-world datasets demonstrate that the proposed CODT outperforms other baselines.