Hate speech on social media is a pressing concern. Understanding the factors associated with hate speech may help mitigate it. Here we explore the association between hate speech and exposure to fake news by studying the correlation between exposure to news from low-credibility sources through following connections and the use of hate speech on Twitter. Using news source credibility labels and a dataset of posts with hate speech targeting various populations, we find that hate speakers are exposed to lower percentages of posts linking to credible news sources. When taking the target population into account, we find that this association is mainly driven by anti-semitic and anti-Muslim content. We also observe that hate speakers are more likely to be exposed to low-credibility news with low popularity. Finally, while hate speech is associated with low-credibility news from partisan sources, we find that those sources tend to skew to the political left for antisemitic content and to the political right for hate speech targeting Muslim and Latino populations. Our results suggest that mitigating fake news and hate speech may have synergistic effects.