Rosen is the son of Sidney and Estelle Rosen, both of whom are psychiatrists. He has been married to Christine Rosen (formerly Stolba), a historian, since 2003. He graduated summa cum laude from Harvard University and was a Marshall scholar at Oxford University, from which he received a second bachelor's degree. He also has a law degree from Yale Law School.

He is a professor of law at George Washington University Law School in Washington, D.C. and has been the commentator on legal affairs for The New Republic since 1992. Rosen is a Nonresident Senior Fellow at the Brookings Institution, where he speaks and writes about Technology and the Future of Democracy. He often appears as a guest on National Public Radio, and is a frequent contributor to The New York Times Magazine.

Rosen has written frequently about the United States Supreme Court. He has interviewed Chief Justice John Roberts, Justice John Paul Stevens, and Justice Stephen Breyer. Justice Ruth Bader Ginsburg credited his early support for her Supreme Court candidacy as a factor in her nomination. More recently, an essay posted on The New Republic website about Sonia Sotomayor, the then-potential nominee for the Supreme Court, provoked controversy for using anonymous sources. Other media outlets, however, including the New York Times, had relied upon similar sources. Rosen has known Justice Elena Kagan for many years and is the brother-in-law of Neal Katyal, the acting Solicitor General. In an opinion piece published after Kagan's nomination hearings and before the Senate's vote on her confirmation, Rosen encouraged Kagan to look to former Justice Louis Brandeis as a model "to develop a positive vision of progressive jurisprudence in an age of economic crisis, financial power and technological change."

Rosen's articles assessing the Supreme Court have been ideologically unpredictable. He strongly denounced Bush v. Gore, but supported the nomination of Chief Justice Roberts, while opposing that of Justice Alito. He supported Sotomayor's confirmation, and has written stories for the New York Times Magazine about the Court's pro-business and anti-regulatory agenda.

Rosen also writes frequently about the effects of technology on privacy and liberty, including articles about privacy in the Internet Age, surveillance cameras in Britain, data mining in Silicon Valley, technology and the Constitution, the effect of neuroscience on the law, DNA databases and genetic surveillance, and Google and the future of free speech.