He was selected by the Raiders in the fourth round of the 1972 NFL draft after playing college football for the Colorado Buffaloes.

In the postseason, he had his best game for the AFC Championship, where he caught nine passes for 186 yards and a touchdown, but the Raiders lost to the Pittsburgh Steelers 24–13.

That year, the Raiders won their first championship, and Branch caught nine combined passes in three games for under 50 yards each, but they still prevailed in the Super Bowl regardless.

[10] After having caught 212 passes for 3,967 yards and 43 touchdowns in his first six years, Branch played the remaining eight seasons with steady but eventual decline.

[11] 1983 would see the Los Angeles Raiders rather easily defeat Pittsburgh and Seattle in the AFC playoffs to make Super Bowl XVIII where they would play the defending champion Washington Redskins.

[14] He held the NFL career playoff records for receptions and receiving yards,[15] which stood until they were broken by Jerry Rice in 1993 and 1994, respectively, while with the San Francisco 49ers.

[13] He was cited by the NFL Network as #5 on players not in the Pro Football Hall of Fame, noted for his speed at the position of wide receiver while being overshadowed by receivers of his time like Pittsburgh rivals Lynn Swann, John Stallworth, and teammate Fred Biletnikoff.

Minus Swann (whose numbers were considerably lower), Branch had comparable statistics to each of those players as each have over 500 receptions and 8,000 yards.

[21] On August 24, 2021, Branch was posthumously selected as the seniors finalist for the Pro Football Hall of Fame Class of 2022.