Green’s Dictionary of Slang

1. (US) to tell someone to be quiet.

1896		H. Blossom Checkers 48: If this hard luck story of mine gets tiresome to you, ring me off.
1908		E. Dyson ‘Two Battlers and a Bear’ in Lone Hand (Sydney) June 176/2: ‘Oh, ring off, parson, ’n’ give the other bloke a charnce’.
1914		Sport (Adelaide) 21 Aug. 2/3: Ring off, Dick, good shots like you are not wanted.

2. (Aus./US) to restrain oneself.

1901		W.A. Sun. Times (Perth) 17 Nov. 1/1: Each managed to let the ‘financial’ female know of their separate desire to die for her love (and lucre) [and] both have been obliged to ‘ring off’ in their attention to damsels in other quarters.
195		Day Book (Chicago) 15 mar. 14/2: The best advice I could give him was to ‘ring off’.

3. to stop talking (other than on a telephone).

1910		Magnet 3 Sept. 16: I’ll ring off while Bulstrode talks wisdom.
1915		D.W. King letter 5 Dec. in L.M. 8046 (1927) 100: This letter is getting so long that I already have grave doubts if the censors will let it by, so I think I will ring off.
1922		E.E. Cummings Enormous Room (1928) 32: ‘Maybe we’d better ring off, or you’ll get in wrong with —’ he indicated t-d with a wave of his head.