In this paper, we present ArCOV-19, an Arabic COVID-19 Twitter dataset that covers the period from 27th of January till 31st of March 2020. ArCOV-19 is the first publicly-available Arabic Twitter dataset covering 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. Preliminary analysis shows that ArCOV-19 captures rising discussions associated with the first reported cases of the disease as they appeared in the Arab world. In addition to the source tweets and the propagation networks, we also release the search queries and the language-independent crawler used to collect the tweets to encourage the curation of similar datasets.