This paper is concerned with the question of how novel digital technologies can be used to enable IT governance to better deal with the need for more agility, flexibility, adaptivity, and connectivity, as brought about by our modern day society. We propose to digitally transform IT governance, in particular making it smart(er) by following a data-driven approach. In line with this, we present a vision for digitally transformed IT governance in the form of the DT4GITM (Digital Twin for Governed IT Management) framework, which exploits the Digital Twin concept as it is already used in other fields to monitor, analyze, simulate, and predict the performance of real-world assets. The purpose of the DT4GITM framework is to serve as a reference architecture for a technological infrastructure based on the Digital Twin concept that connects three interrelated systems -the IT governance processes, the governed IT management processes, and the managed organizational IT assets.