Professor Graber held a faculty position in the Department of Government and Politics at the University of Maryland, College Park, from 1993 to 2007 and taught at the University of Maryland School of Law as an adjunct professor beginning in the fall of 2002. In 2004, he was appointed Professor of Government and Law at Maryland Carey Law, a title he held until May 1, 2015, at which time he received an appointment as the Jacob A. France Professor of Constitutionalism. In 2016, he was named Regents Professor, one of only seven Regents Professors in the history of the University System of Maryland and the only Regents Professor on the UMB campus. He served as associate dean for research and faculty development from 2010 to 2013. He has also been one of the organizers of the annual Constitutional Law "Schmooze," which attracts scholars from across the country to the law school.

Professor Graber is recognized as one of the leading scholars in the country on constitutional law and politics. He is the author of A New Introduction to American Constitutionalism (Oxford 2013), Dred Scott and the Problem of Constitutional Evil (Cambridge, 2006), and co-editor (with Keith Whittington and Howard Gillman) of American Constitutionalism: Structures and Powers and American Constitutionalism: Rights and Powers, both also from Oxford University Press, and co-editor with Mark Tushnet and Sandy Levinson of Constitutional Democracy in Crisis (Oxford 2018). His most recent book is Punish Treason, Reward Loyalty: The Forgotten Goals of Constitutional Reform After the Civil War (Kansas, 2023).

Professor Graber is also the author of over 100 articles, including "The Non-Majoritarian Problem: Legislative Deference to the Judiciary" in Studies in American Political Development, "Naked Land Transfers and American Constitutional Development," published in the Vanderbilt Law Review and "Resolving Political Questions into Judicial Questions: Tocqueville’s Aphorism Revisited," published by Constitutional Commentary.

He has been a visiting faculty member at Harvard University, Yale Law School, the University of Virginia School of Law, the University of Pennsylvania, the University of Toronto, the University of Oregon School of Law, and Simon Reichman University.