How human-like do conversational robots need to look to enable long-term human-robot conversation? One essential aspect of long-term interaction is a human's ability to adapt to the varying degrees of a conversational partner's engagement and emotions. Prosodically, this can be achieved through (dis)entrainment. While speech-synthesis has been a limiting factor for many years, restrictions in this regard are increasingly mitigated. These advancements now emphasise the importance of studying the effect of robot embodiment on human entrainment. In this study, we conducted a between-subjects online human-robot interaction experiment in an educational use-case scenario where a tutor was either embodied through a human or a robot face. 43 English-speaking participants took part in the study for whom we analysed the degree of acoustic-prosodic entrainment to the human or robot face, respectively. We found that the degree of subjective and objective perception of anthropomorphism positively correlates with acoustic-prosodic entrainment.