Conversation is a primary means of social influence, but its effects on brain activity remain unknown. Previous work on conversation and social influence has emphasized public compliance, largely setting private beliefs aside. Here, we show that consensus-building conversation aligns future brain activity within groups, with alignment persisting through novel experiences participants did not discuss. Participants watched ambiguous movie clips during fMRI scanning, then conversed in groups with the goal of coming to a consensus about each clip's narrative. After conversation, participants' brains were scanned while viewing the clips again, along with novel clips from the same movies. Groups that reached consensus showed greater similarity of brain activity after conversation. Participants perceived as having high social status spoke more and signaled disbelief in others, and their groups had unequal turn-taking and lower neural alignment. By contrast, participants with central positions in their real-world social networks encouraged others to speak, facilitating greater group neural alignment. Socially central participants were also more likely to become neurally aligned to others in their groups.