Service robots are increasingly deployed in various industries including tourism. In spite of extensive research on the user’s experience in interaction with these robots, there are yet unanswered questions about the factors that influence user’s compliance. Through three online studies, we investigate the effect of the robot anthropomorphism and language style on customers’ willingness to follow its recommendations. The mediating role of the perceived mind and persuasiveness in this relationship is also investigated. Study 1 (n = 89) shows that a service robot with a higher level of anthropomorphic features positively influences the willingness of users to follow its recommendations while language style does not affect compliance. Study 2a (n = 168) further confirms this finding when we presented participants with a tablet vs. a service robot with an anthropomorphic appearance while communication style does not affect compliance. Finally, Study 2b (n = 122) supports the indirect effect of anthropomorphism level on the willingness to follow recommendations through perceived mind followed by persuasiveness. The findings provide valuable insight to enhance human–robot interaction in service settings.