Self-promotion in science is ubiquitous but may not be exercised equally by everyone. Research on self-promotion in other domains suggests that, partly due to adverse reactions to non-gender-conforming career-enhancing behaviors, women tend to self-promote less often than men. We test whether this pattern extends to online spaces by examining scholarly self-promotion over six years using 23M tweets about 2.8M research papers authored by 3.5M scientists. We find that, overall, women are about 28% less likely than men to self-promote their papers on Twitter (now X) despite accounting for important confounds. The differential adoption of Twitter does not fully explain the gender gap in self-promotion, which is large even in relatively gender-balanced research areas, where adversity is expected to be smaller. Moreover, we find that the gender gap increases with higher performance and academic status, being most pronounced for research-prolific women from top-ranked institutions who publish papers in high-impact journals. We also find differential returns with respect to gender: while self-promotion is associated with increased tweets of papers compared to no self-promotion, the increase is slightly smaller for women than for men. Our findings reveal that scholarly self-promotion online varies meaningfully by gender and can contribute to a measurable gender gap in the visibility of scientific ideas.