Dorsen is a graduate of Harvard Law School, where he was an editor of the Harvard Law Review. During his military service in the office of the general counsel to the Secretary of the Army he assisted in fighting McCarthyism during the 1954 Army-McCarthy Hearings. He served as law clerk to Chief Judge Calvert Magruder of the U.S. Court of Appeals for the First Circuit and to Supreme Court Justice John Marshall Harlan.

He is the author or editor of many articles and books (sometimes with others), including Frontiers of Civil Liberties (1968), The Rights of Americans (1971), Political and Civil Rights in the U.S. (1967 and 1976/1979 editions), The Evolving Constitution (1987), Human Rights in Northern Ireland (1991), Democracy and The Rule of Law (2000) and The Unpredictable Constitution (2001).

Dorsen served as president of the American Civil Liberties Union 1976-91. Earlier, while general counsel to the ACLU 1969-76, he participated in dozens of Supreme Court cases, arguing among others those that won for juveniles the right to due process, upheld constitutional rights of nonmarital children, and advanced abortion rights. He helped write petitioner's brief in Roe v. Wade and appeared amicus curiae in the Gideon case, the Pentagon Papers case and the Nixon Tapes case.

Dorsen was the founding president of the Society of American Law Teachers in 1973. He was chairman of the Lawyers Committee for Human Rights 1996-2000 and since 1996 he has been the founding president of the U.S. Association of Constitutional Law, an affiliate of the International Association of Constitutional Law. He has chaired two U.S. Government commissions, has received many awards and honorary degrees, including the Presidential Eleanor Roosevelt Award for Human Rights, and he is a Fellow of the American Academy of Arts and Sciences and a member of the Council on Foreign Relations.