End-to-end (E2E) autonomous driving has recently emerged as a new paradigm, offering significant potential. However, few studies have looked into the practical challenge of deployment across domains (e.g., cities). Although several works have incorporated Large Language Models (LLMs) to leverage their open-world knowledge, LLMs do not guarantee cross-domain driving performance and may incur prohibitive retraining costs during domain adaptation. In this paper, we propose RoCA, a novel framework for robust cross-domain E2E autonomous driving. RoCA formulates the joint probabilistic distribution over the tokens that encode ego and surrounding vehicle information in the E2E pipeline. Instantiating with a Gaussian process (GP), RoCA learns a set of basis tokens with corresponding trajectories, which span diverse driving scenarios. Then, given any driving scene, it is able to probabilistically infer the future trajectory. By using RoCA together with a base E2E model in source-domain training, we improve the generalizability of the base model, without requiring extra inference computation. In addition, RoCA enables robust adaptation on new target domains, significantly outperforming direct finetuning. We extensively evaluate RoCA on various cross-domain scenarios and show that it achieves strong domain generalization and adaptation performance.