Autism is a neurodevelopmental disorder that affects the everyday life of people who have this lifelong condition. Robots hold great promise for uplifting therapy and care of the affected population. We searched Scopus, Medline, ScienceDirect, Web of Science, and PubMed databases for randomized controlled trials that had evaluated robot use in the therapy of people with autism, to see how effective social robots have been incorporated in autism care. Out of 240 papers initially identified, 19 satisfied the inclusion criteria and were fully evaluated. Overall, 10 different robots were utilized in the trials, out of which, four were non-humanoids. The number of papers with positive results for using robots on the main and secondary parameters was 11 and 5, respectively. Three papers reported that robot groups did not achieve better results than others. Robots in the papers included here were mainly added as the "entertainment agent" to elicit greater engagement from the participants, which is understandable, as robots at this stage might not be ready yet to deliver high-end care.