Arthur Branch is a fictional character on the TV crime drama Law & Order and one of its spinoffs, Law & Order: Trial by Jury. Branch has also appeared on Law & Order: Special Victims Unit, Law & Order: Criminal Intent, and Conviction. He appeared in 142 episodes of the various series in the franchise (116 episodes of Law & Order, 11 episodes of Law & Order: Special Victims Unit, one episode of Law & Order: Criminal Intent, all 13 episodes of Law & Order: Trial by Jury, and the pilot episode of Conviction).

Branch was portrayed by Fred Thompson, who started his acting career in 1985, and was a sitting U.S. Senator by the time Arthur Branch was introduced to the Law & Order franchise as the Manhattan District Attorney in the 2002 episode "American Jihad". In 2005, during his third season on Law & Order, his character appeared in the main cast of Trial by Jury, making him one of the few actors to be in the main cast on two TV series simultaneously as the same character. When Thompson began the role, his term in the Senate did not expire until several months after his first episode aired—thus making Thompson the first sitting U.S. Senator to portray someone other than himself on TV.

Thompson was the only regular on Law & Order who was once a prosecutor in real life. He worked as an assistant United States Attorney from 1969 to 1972.

Branch graduated from Yale University and Yale Law School. He was later a professor at the latter. He and his wife, Lillian, have lived in New York City since moving in the early 1980s from the state of Georgia. According to McCoy, Lillian "loves the smell of concrete", and would not allow Arthur to move from New York City back to Georgia. Arthur and Lillian have at least one child, a son named Bobby. They also have a grandson and a granddaughter named Maggie. He also has a nephew named Andy. He owns a Chevrolet and a Porsche. He speaks with a Southern accent and commonly uses colorful metaphors.

Branch is elected the Manhattan District Attorney in 2002, replacing Nora Lewin (Dianne Wiest). Prior to becoming the District Attorney, he was successful as a lawyer and became the head of his New York law firm. He says that he was elected DA because the people of Manhattan wanted to feel safe after the September 11 attacks. Along with Odafin Tutuola (Ice-T), he and Abbie Carmichael (Angie Harmon) are the only characters in the show known to be Republicans. Branch's administration is a sharp contrast to that of Lewin, as he supports the death penalty and does not believe in the existence of a constitutional right to privacy. He had written a book on the justice system and represented the Chinese government when he worked in private practice.

His legal and political conservatism often puts him in conflict with Jack McCoy (Sam Waterston), a relative center leftist, as well as his previous assistant DA Serena Southerlyn (Elisabeth Röhm), a liberal idealist. He has few quarrels with Alexandra Borgia (Annie Parisse), who is more conservative in her viewpoints than Southerlyn. He is portrayed as having an amicable working relationship with ADA Connie Rubirosa (Alana de la Garza).

He strongly supported the Iraq War. He does not oppose same-sex marriage, nor does he particularly approve of it; he believes that it is none of his business nor that of the U.S. federal government. While his legal philosophy is decidedly conservative, he is not blindly partisan; he ascribes cynical, political motives to drug prohibition, refers to the U.S. National Guard as "the Dan Quayle Brigade", and is not averse to seeking alternatives to the death penalty when he thinks it appropriate.

Although he is personally pro-life, he describes himself as even more "pro-law", and orders Olivia Benson (Mariska Hargitay) and Casey Novak (Diane Neal) to arrest a doctor who deliberately misled a young pregnant woman to ensure her pregnancy would develop past the legal time limit for the procedure, thus prompting her to desperately ask her boyfriend to assault her to induce a still birth.