Self-promotion in science is ubiquitous but may not be exercised equally by men and women. Research on self-promotion in other domains suggests that, due to bias in self-assessment and adverse reactions to non-gender-conforming behaviors (``pushback''), women tend to self-promote less often than men. We test whether this pattern extends to scholars by examining self-promotion over six years using 23M Tweets about 2.8M research papers by 3.5M authors. Overall, women are about 28% less likely than men to self-promote their papers even after accounting for important confounds, and this gap has grown over time. Moreover, differential adoption of Twitter does not explain the gender gap, which is large even in relatively gender-balanced broad research areas, where bias in self-assessment and pushback are expected to be smaller. Further, the gap increases with higher performance and status, being most pronounced for productive women from top-ranked institutions who publish in high-impact journals. Critically, we find differential returns with respect to gender: while self-promotion is associated with increased tweets of papers, the increase is smaller for women than for men. Our findings suggest that self-promotion varies meaningfully by gender and help explain gender differences in the visibility of scientific ideas.