ArCOV-19 is an Arabic COVID-19 Twitter dataset that covers the period from the 27th of January till the 31st of March 2020. It is the first publicly-available Arabic Twitter dataset covering the COVID-19 pandemic that includes around 748k popular tweets (according to Twitter search criterion) alongside the propagation networks of the most-popular subset of them. The propagation networks include both retweets and conversational threads (i.e., threads of replies). ArCOV-19 is designed to enable research under several domains including natural language processing, information retrieval, and social computing, among others. In addition to that, ArCOV-19 contains the search queries and the language-independent crawler used to collect the tweets to encourage the curation of similar datasets.