Aside from the offensive meaning, colloquial British English uses the term fag to indicate a cigarette.
James has gone outside for a fag
In my googling, I thought perhaps this originates from one of the possible meanings of faggot:
a bundle of sticks, twigs, or branches bound together and used as fuel, a fascine, a torch, etc.
In a very loose sense, this definition could be applied to a cigarette. It's a collection of materials (tar, tobacco, etc) bound together for burning.
The origin from Etymonline indicates:
1888, probably from fag "loose piece, last remnant of cloth" (late 14c., as in fag-end "extreme end, loose piece," 1610s)
This appears to be speculative, and doesn't necessarily explain why this definition fell into common usage to indicate a cigarette. I'm looking for something more concrete indicating what caused it to be used in this context.
What is the origin of this meaning of the word?
Best Answer
According to the Online Etymology Dictionary, it comes from "fag", meaning a loose piece of cloth:
The OED is a bit more convinced and categorically links it to fag-end:
Fag-end itself, always according to the OED, comes from an usage of fag, meaning "something that hangs loose". I read all this as suggesting that the word for cigarette came about because of the way cigarettes often hang from smokers' mouths. For a famous example, see Lucky Luke: