In human relationships, responsiveness---behaving in a sensitive manner that is supportive of another person's needs---plays a major role in any interaction that involves effective communication, caregiving, and social support. Perceiving one's partner as responsive has been tied to both personal and relationship well-being. In this work, we examine whether and how a robot's behavior can instill a sense of responsiveness, and the effects of a robot's perceived responsiveness on the human's perception of the robot. In an experimental between-subject study (n=34), a desktop non-anthropomorphic robot performed either positive or negative responsiveness behaviors across two modalities (simple gestures and written text) in response to participants' negative event disclosure. We found that perceived partner responsiveness, positive human-like traits, and robot attractiveness were higher in the positively responsive condition. This has design implications for interactive robots, in particular for robots in caregiving roles.