Self-driving cars are expected to be integrated into the traffic system in the near future. It is crucial to understand how the public accepts self-driving cars and how adoption rates are influenced. The main purpose of this study was to investigate how trait anxiety and the Big Five personality traits affect acceptance and to provide a personality profile of early adopters of self-driving cars. A total of 527 drivers participated in the research, completing Chinese versions of the Self-driving Car Acceptance Scale, the Trait Anxiety Inventory, and the Big Five Inventory and some demographic questions. The results showed that trait anxiety had a positive effect on perceived automation reliability. Openness and extraversion had positive effects on self-driving car acceptance, while neuroticism had a negative effect. People with high agreeableness had a more positive perspective on the benefits of self-driving cars, but they were also more worried about ease of use and automation reliability. These results help to provide a personality profile of early adopters of self-driving cars. People with certain personality traits are more likely to be starting points for the diffusion of self-driving cars.