Research has shown that accounting for moral sentiment in natural language can yield insight into a variety of on- and off-line phenomena such as message diffusion, protest dynamics, and social distancing. However, measuring moral sentiment in natural language is challenging, and the difficulty of this task is exacerbated by the limited availability of annotated data. To address this issue, we introduce the Moral Foundations Twitter Corpus, a collection of 35,108 tweets that have been curated from seven distinct domains of discourse and hand annotated by at least three trained annotators for 10 categories of moral sentiment. To facilitate investigations of annotator response dynamics, we also provide psychological and demographic metadata for each annotator. Finally, we report moral sentiment classification baselines for this corpus using a range of popular methodologies.