The aim of the current study was to investigate children's brain responses to robot-assisted language learning. EEG brain signals were collected from 41 Japanese children who learned French vocabularies in two groups; half of the children learned new words from a social robot that narrated a story in French using animations on a computer screen (Robot group) and the other half watched the same animated story on the screen but only with a voiceover narration and without the robot (Display group). To examine brain activation during the learning phase, we extracted EEG functional connectivity (FC) which is defined as the rhythmic synchronization of signals recorded from different brain areas. The results indicated significantly higher global synchronization of brain signals in the theta frequency band in the Robot group during the learning phase. Closer inspection of intra-hemispheric and inter-hemispheric connections revealed that children who learned a new language from the robot experienced a stronger theta-band EEG synchronization in inter-hemispheric connections, which has been previously associated with success in second language learning in the neuroscientific literature. Additionally, using a multiple linear regression analysis, it was found that theta-band FC and group assignment were significant predictors of children's language learning with the Robot group scoring higher in the post-interaction word recognition test. These findings provide novel neuroscientific evidence for the effectiveness of social robots as second language tutors for children.