(1) Background: Social robot interaction design is crucial for determining user acceptance and experience. However, few studies have systematically discussed the current focus and future research directions of social robot interaction design from a bibliometric perspective. Therefore, we conducted this study in order to identify the latest research progress and evolution trajectory of research hotspots in social robot interaction design over the last decade. (2) Methods: We conducted a comprehensive review based on 2416 papers related to social robot interaction design obtained from the Web of Science (WOS) database. Our review utilized bibliometric techniques and integrated VOSviewer and CiteSpace to construct a knowledge map. (3) Conclusions: The current research hotspots of social robot interaction design mainly focus on #1 the study of human–robot relationships in social robots, #2 research on the emotional design of social robots, #3 research on social robots for children’s psychotherapy, #4 research on companion robots for elderly rehabilitation, and #5 research on educational social robots. The reference co-citation analysis identifies the classic literature that forms the basis of the current research, which provides theoretical guidance and methods for the current research. Finally, we discuss several future research directions and challenges in this field.