The question of why socially monogamous females engage in extra‐pair behaviour is long‐standing in evolutionary biology. Due to a lack of empirical support among passerine birds, recent work has moved away from the indirect‐benefits hypothesis to explain extra‐pair mating behaviour by females, instead favouring the hypothesis that this is the result of a pleiotropic effect. That is, a trait under strong positive selection in either or both sexes are genetically linked with another, potentially unrelated, trait. For example, genes beneficial to female fecundity (that promote within‐pair solicitation of mating from a male partner) might also lead to extra‐pair behaviour (by also promoting solicited copulations from extra‐pair males). Here, we test two predictions from this hypothesis: We test the prediction that female divorce, measured as the number of social mates within a given year, is linked with 1) the number of extra‐pair males engaged by the female and 2) the proportion of the female's offspring that are extra‐pair. Our results show that females who divorce their social partner are more likely to produce extra‐pair offspring than those who maintain social monogamy, supporting the pleiotropy hypothesis. However, those females did not also have a higher proportion of extra‐pair offspring. The number of broods initiated was also positively correlated with the number of extra‐pair males that sired a female's offspring, probably through increased opportunity for extra‐pair males to sire offspring over a longer breeding season. Our results support the intrasexual pleiotropy hypothesis as a driver of female extra‐pair behaviour.