This paper presents a socially interactive humanoid robot-assisted system for sign language (SL) tutoring for children with communication impairments by means of imitation-based interaction games. In this study, a five-fingered robot platform Robovie R3 is used to express a set of chosen words in Turkish sign language (TSL) using hand and body movements combined with facial expressions. The robot is able to recognize signs through a RGB-D camera and give vocal, visual and motional (as signs) feedback. The proposed game consists of an introductory phase where participants are introduced to the robot and the signs; an imitation-based learning phase where participants are motivated to imitate the signs demonstrated by the robot, and a test phase where the signs taught in the previous phases are tested within a guessing game. The current paper presents results from the studies with three different test groups. The presented humanoid robot is used as an assistive social companion in the game context using sign language and visual clues to interact with the children. The robot is evaluated according to the participant's sign recognition ability within different setups. The results indicate that the robot has a significant effect on the sign learning performance of participants.