His uncle Jozsef Berger was killed at the Majdanek concentration camp, and his maternal aunt Irma died at the Auschwitz concentration camp in 1942. He was raised Roman Catholic.

Branca was exempted from military service during World War II, due to his asthma and a punctured eardrum. After Branca attended a tryout with the Brooklyn Dodgers in 1943, the team signed him to a contract. He debuted in the major leagues at age 18 on June 12, 1944, and put up a 3.04 earned run average (ERA) in 109⁄3 innings pitched in his rookie year.

A three-time All-Star, Branca won 80 games for the Dodgers with a career-high 21 wins in 1947. In 1948, he was ninth in the league in wins (14) and won–lost percentage (.609). In 1949, he led the National League (NL) in won-lost percentage (.722). In 1951, he was tenth in the NL in ERA (3.26).

Branca married Ann Mulvey, whose parents were part-owners of the Dodgers, in 1951, shortly after giving up the famous home run. Their daughter, Mary, married baseball player Bobby Valentine. Their other daughter Patti lives in Fort Myers, Florida. Branca released a memoir in 2011, titled A Moment in Time.

A back injury suffered during spring training in 1952 limited Branca’s effectiveness thereafter. Branca appeared in only 12 games for the Dodgers during the 1952 season. In the eighth inning of Game 7 of the 1952 World Series against the New York Yankees, Branca was ejected from the dugout by home plate umpire Larry Goetz for bench jockeying. Branca was only the second player in MLB history to be ejected from a World Series, and the first who was not actually in the game at the time. He did not make an appearance in the series.

Branca began the 1953 season with Brooklyn, but was claimed off waivers by the Detroit Tigers on July 10, 1953. The Tigers released Branca in July 1954. After he pitched batting practice for the Yankees, the Yankees signed him, and used him in five games later in the season. Branca pitched for the Minneapolis Millers in 1955, but was released due to ineffectiveness caused by an arm injury.

In 1956, Branca appeared at Old Timer’s Day for the Yankees, believing his career was over. His pitching velocity returned, and he signed with the Dodgers for the last month of the season, making one appearance.

Branca was a contestant on Concentration starting in 1963, where he won 17 consecutive games. He appeared in Concentration’s 1963 Challenge of Champions.

Branca was a pallbearer at Jackie Robinson’s funeral in October 1972.

Branca became friends with Thomson, a bond that lasted into each man’s old age, including joint television and trade show appearances. Branca later learned from Detroit Tiger Ted Gray that the Giants had stolen the signs to the two pitches he threw Thomson. That rumor was confirmed in The Wall Street Journal in 2001, when Giant Sal Yvars admitted that he relayed to Thomson the stolen signs for Branca’s fastballs. Joshua Prager detailed the revelations in a book entitled The Echoing Green: The Untold Story of Bobby Thomson, Ralph Branca and The Shot Heard Round the World. Thomson acknowledged to Prager that the Giants had stolen signs in 1951 but denied that he had foreknowledge of the pitch he hit off Branca for the pennant-winning home run. According to Branca, Thomson admitted to accepting the stolen signs during his first three at-bats of that game, but claimed that he did not do so in the final at-bat; Branca indicated that he did not believe Thomson’s denials and remained convinced that Thomson was in fact tipped off on the fateful pitch.

In the 2012 movie, Parental Guidance, Branca made a cameo appearance as a judge during a scene involving an audition for a music school. During the scene Billy Crystal’s grandson takes to the stage and recites the radio broadcast of, “The Shot Heard Round the World.” Branca was portrayed by Hamish Linklater in the 2013 film 42, a biographical sports drama about Robinson’s career. Branca was the subject of the 2013 documentary “Branca’s Pitch,” produced by Andrew J. Muscato.