Green’s Dictionary of Slang

1. (US) cheering, encouraging, supporting one’s sports team.

1889		World (N.Y.) 18 Oct. 2/1: The New Yorks and Brooklyns will meet for the first time in a fight for the world’s championship, and the combined enthusiasm and crankdom of the two cities will be massed on the available sitting and standing room of the inclosure. And how the Partisan will ‘root’! There will be ‘rooting’ singular and ‘rooting’ plural, ‘rooting’ masculine and ‘rooting’ feminine. ‘rooting’ young, and ‘rooting’ old.
1908		N.Y. Tribune 19 July 42: [advert] Rah! Rah! Rah! Good Work!! Whew! but this rooting proposition is thirst raising.
1913		Day Book (Chicago) 20 July 13: There is still the old excitement and the rooting and the fun, / Whether watching arrant ‘bushers’ or the Giants.
1938		D. Runyon ‘A Piece of Pie’ in Runyon on Broadway (1954) 685: No talking and no rooting from the spectators is permitted.

2. attrib. use of sense 1.

1977		(con. 1949) J.G. Dunne True Confessions (1979) 54: Jack would have a rooting interest in whoever was the new chairman of the Building Fund.
1997		Simon & Burns Corner (1998) 122: Sitting courtside with a small coterie of teenaged girls and younger boys — a rooting gallery for the M.L.K. team.