Most social groups punish freeriders (i.e., individuals who receive the same benefits from the group as others, despite contributing less to its success). In small groups, individual group members (rather than established authorities) typically implement this punishment spontaneously, and punishers may consequently be awarded social status by their peers. Here, we tested the preregistered hypothesis that this way of acquiring status works best when fellow group members are high, rather than low, in right-wing authoritarianism (RWA). The hypothesis was supported in a laboratory-based behavioral study (N = 667) in which small groups interacted in a financially incentivized repeated public goods game involving punishment (i.e., a social dilemma that puts immediate individual benefits at odds with long-term collective interests). Linking the process of status acquisition to peer RWA significantly advances the understanding of social dynamics in small groups.