This article assesses the usefulness for social media research of controversy analysis, an approach developed in Science and Technology Studies (STS) and related fields. We propose that this approach can help to address an important methodological problem in social media research, namely, the tension between social media as resource for social research and as an empirical object in its own right. Initially developed for analyzing interactions between science, technology, and society, controversy analysis has in recent decades been implemented digitally to study public debates and issues dynamics online. A key feature of controversy analysis as a digital method, we argue, is that it enables a symmetrical approach to the study of media-technological dynamics and issue dynamics. It allows us to pay equal attention to the ways in which a digital platform like Twitter mediates public issues, and to how controversies mediate “social media” as an object of public attention. To sketch the contours of such a symmetrical approach, the article discusses examples from a recent social media research project in which we mapped issues of “privacy” and “surveillance” in the wake of the National Security Agency (NSA) data leak by Edward Snowden in June 2013. Through a discussion of social media research practice, we then outline a symmetrical approach to analyzing controversy with social media. We conclude that the digital implementation of such an approach requires further exchanges between social media researchers and controversy analysts.