Supporting the development of a child with autism is a multi-profile therapeutic work on disturbed areas, especially understanding and linguistic expression used in social communication and development of social contacts. Previous studies show that it is possible to perform some therapy using a robot. This article is a synthesis review of the literature on research with the use of robots in the therapy of children with the diagnosis of early childhood autism. The review includes scientific journals from 2005–2021. Using descriptors: ASD (Autism Spectrum Disorders), Social robots, and Robot-based interventions, an analysis of available research in PubMed, Scopus and Web of Science was done. The results showed that a robot seems to be a great tool that encourages contact and involvement in joint activities. The review of the literature indicates the potential value of the use of robots in the therapy of people with autism as a facilitator in social contacts. Robot-Assisted Autism Therapy (RAAT) can encourage child to talk or do exercises. In the second aspect (prompting during a conversation), a robot encourages eye contact and suggests possible answers, e.g., during free conversation with a peer. In the third aspect (teaching, entertainment), the robot could play with autistic children in games supporting the development of joint attention. These types of games stimulate the development of motor skills and orientation in the body schema. In future work, a validation test would be desirable to check whether children with ASD are able to do the same with a real person by learning distrust and cheating the robot.