There is increasing pressure on social media companies to reduce the spread of misinformation on their platforms. However, they would prefer not to be the arbiters of truth as the truth can be subjective or otherwise hard to determine. Instead, they would prefer that social media users themselves show better discernment when deciding which information to share. Here we show that allowing people to share only those social media posts that they have indicated are true significantly improves sharing discernment, as measured by the difference in the probability of sharing true information versus the probability of sharing false information. Because it doesn’t require social media companies to be the arbiters of truth, this self-censorship intervention can be employed in situations where social media companies suspect that individuals are propagating misinformation but are not sufficiently confident in their suspicions to directly censor the individuals involved. As such, self-censorship can usefully supplement externally imposed (i.e. traditional) censorship in reducing the propagation of false information on social media platforms.