Developments in social robotics raise the prospect of robots coaching and interacting with patient during rehabilitation training assuming a role of a trainer. This raises questions regarding the acceptance of robots in this role and more specifically, to what extent the robot should be anthropomorphic. This paper presents the results of an online experiment designed to evaluate the user acceptance of Socially Assistive Robots (SARs) as rehabilitation trainers, and the effect of anthropomorphism on this matter. User attitudes were surveyed with regards to variations of the robot’s anthropomorphism as a rehabilitation trainer. The results show that 1) participants are accepting towards SAR-assisted rehabilitation therapies, 2) higher anthropomorphism is generally preferred but does not affect patient’s acceptance towards such therapy and technology. Qualitative data brings insight to patient technology acceptance, needs for rehabilitation training and the effect of anthropomorphism.