Green’s Dictionary of Slang

to care; usu. in a negative sense, e.g. who gives a damn? or like I give a damn.

1929		W.D. Edmonds Rome Haul 109: Who gives a dang!
1940		J.H. O’Hara Pal Joey 92: Does he give a damn if I am the only one who can operate the radio.
1953		J. Thompson Savage Night (1991) 138: Go ahead and see if I give a dang.
1972		D. Jenkins Semi-Tough 171: I just don’t give one goddamn how many transplant cases are walking around healthy.
1990		S. Morgan Homeboy 166: [She] could no more pronounce the name of the province pasted on the Army telegram [...] than give a damn.
1999		Indep. Rev. 9 July 15: It all seems [...] so much harder to give a damn about, than before.