Green’s Dictionary of Slang

a general affirmative, OK, I’ll do it.

1972		(con. c.1930) G. Sothern Georgia 329: ‘Tell Georgia I will be around to pick her up at about nine thirty’ ‘Check, Mr. Plant,’ Foxie said. ‘Will do’.
1990		(con. early 1950s) J. Ellroy L.A. Confidential 439: Will do.