In face-to-face interaction, moving with and mimicking the body movements of communication partners has been widely demonstrated to affect interpersonal processes, including feelings of affiliation and closeness. In this paper, we examine effects of movement and mimicry in robot-mediated communication. Participants were instructed to get to know their partner, a confederate, who interacted with them via a telepresence robot. The robot either (a) mimicked the participant's body orientation (mimicry condition), (b) mimicked pre-recorded movements of another participant (random movement condition), or (c) did not move during the interaction (static condition). Results showed that mimicry and random movement had similar effects on participants' perceptions of similarity and closeness to their partners and that these effects depend on the participant's gender and level of self-monitoring. The findings suggest that the social movements of a telepresence robot affect interpersonal processes and that these effects are shaped by individual differences.