The mission of the Open Radio Access Network (O-RAN) Alliance is to evolve RAN for the next-generation network in a way that will embed principles of openness and intelligence. Currently, digital twin (DT) is emerging as a keystone technology for the development of sixth-generation (6G) networks oriented services. This article aims to provide a comprehensive vision of how DT and O-RAN represent two complementary concepts, which when merged will enable the deployment of an intelligent and resilient 6G RAN. In particular, DT will play a crucial role by enhancing the principles of intelligence, autonomy, and openness on which O-RAN is based. A brief overview of both O-RAN and DT concepts is discussed. Subsequently, potential use cases and services delivered through a DT-based O-RAN architecture are illustrated. Challenges and future research directions are also highlighted and discussed.