Abstract: The rapid development of artificial intelligence technology allows robots to have social functions. In the case of human individuals interacting directly with a robot with artificial intelligence, if the individual can perceive the same or similar feelings as they have when interacting with a real human, the robot can be considered to have social presence. Trust is an important factor that affects human–robot collaboration. This research explores the influence of the character and information disclosure of robots on trust in human–robot collaboration as well as the mediating role of social presence. This study uses the Columbia Card Task to design a human–robot cooperative experiment platform. During the experiment, robots provide different levels of character (introversion vs. extroversion) and information disclosure (high disclosure vs. low disclosure). The results show that the character of robots has a significant impact on emotional trust: the higher the level of extroversion is, the stronger the level of human emotional trust. Furthermore, the level of information disclosure by robots has a significant impact on cognitive trust: the higher the level of information disclosure is, the stronger the level of cognitive trust. Social presence has a mediating role in the effect of character on emotional trust and the impact of information disclosure on cognitive trust. The research results can provide suggestions for improving the acceptance of social robots in human–robot collaboration and improving the quality and efficiency of collaborative human–robot task decision-making. Research on robots’ character and information disclosure can provide a theoretical basis for related researchers and developers.