Although robots' social behaviors are known for their capacity to facilitate learner-robot interaction for language learning, their application and effect have not been adequately explored. This study reviewed 59 empirical articles to examine the contexts and application of various social behaviors of robots for language learning, and conducted a meta-analysis of 18 study samples to evaluate the effect of robots' social supportive behaviors on language learning achievement. Results indicate that robots' social behaviors have mostly been applied in the studies with K-12 students, for learning vocabulary in English, including small sample sizes of below 80 participants, and lasting for one session. Second, various verbal and non-verbal behaviors of robots have been identified and applied, showing mixed results on language learning achievement. Third, robots' social supportive behaviors have produced a positive effect on language learning achievement compared to neutral behaviors (g = 0.269). Finally, detailed suggestions for future research are discussed.