This paper presents a new method for identifying scholars who have a Twitter account from bibliometric data from Web of Science (WoS) and Twitter data from Altmetric.com. The method reliably identifies matches between Twitter accounts and scholarly authors. It consists of a matching of elements such as author names, usernames, handles, and URLs, followed by a rule-based scoring system that weights the common occurrence of these elements related to the activities of Twitter users and scholars. The method proceeds by matching the Twitter accounts against a database of millions of disambiguated bibliographic profiles from WoS. This paper describes the implementation and validation of the matching method, and performs verification through precision-recall analysis. We also explore the geographical, disciplinary, and demographic variations in the distribution of scholars matched to a Twitter account. This approach represents a step forward in the development of more advanced forms of social media studies of science by opening up an important door for studying the interactions between science and social media in general, and for studying the activities of scholars on Twitter in particular.