Te reo Māori, the Indigenous language of Aotearoa New Zealand, is a distinctive feature of the nation’s cultural heritage. This paper documents our efforts to build a corpus of 79,000 Māori-language tweets using computational methods. The Reo Māori Twitter (RMT) Corpus was created by targeting Māori-language users identified by the Indigenous Tweets website, pre-processing their data and filtering out non-Māori tweets, together with other sources of noise. Our motivation for creating such a resource is three-fold: (1) it serves as a rich and unique dataset for linguistic analysis of te reo Māori on social media; (2) it can be used as training data to develop and augment Natural Language Processing (NLP) tools with robust, real-world Māori-language applications; and (3) it will potentially promote awareness of, and encourage positive interaction with, the growing community of Māori tweeters, thereby increasing the use and visibility of te reo Māori in an online environment. While the corpus captures data from 2007 to 2020, our analysis shows that the number of tweets in the RMT Corpus peaked in 2014, and the number of active tweeters peaked in 2017, although at least 600 users were still active in 2020. To the best of our knowledge, the RMT Corpus is the largest publicly-available collection of social media data containing (almost) exclusively Māori text, making it a useful resource for language experts, NLP developers and Indigenous researchers alike.