Humans and other primates have evolved the ability to represent their status in the group's social hierarchy, which is essential for avoiding harm and accessing resources. Yet it remains unclear how the human brain learns dominance status and adjusts behavior accordingly during dynamic social interactions. Here we address this issue with a combination of fMRI and transcranial direct current stimulation (tDCS). In a first fMRI experiment, participants learned an implicit dominance hierarchy while playing a competitive game against three opponents of different skills. Neural activity in the rostromedial PFC (rmPFC) dynamically tracked and updated the dominance status of the opponents, whereas the ventromedial PFC and ventral striatum reacted specifically to competitive victories and defeats. In a second experiment, we applied anodal tDCS over the rmPFC to enhance neural excitability while subjects performed a similar competitive task. The stimulation enhanced the relative weight of victories over defeats in learning social dominance relationships and exacerbated the influence of one's own dominance over competitive strategies. Importantly, these tDCS effects were specific to trials in which subjects learned about dominance relationships, as they were not present for control choices associated with monetary incentives but no competitive feedback. Taken together, our findings elucidate the role of rmPFC computations in dominance learning and unravel a fundamental mechanism that governs the emergence and maintenance of social dominance relationships in humans.