"male homosexual," 1914, Amer.Eng. slang (shortened form fag is from 1921), probably from earlier contemptuous term for "woman" (1591), especially an old and unpleasant one, in reference to faggot
(1) "bundle of sticks," as something awkward that has to be carried (cf. baggage).
It was used in this sense in 20c. by D.H. Lawrence and James Joyce, among others. It may also be reinforced by Yiddish faygele "homosexual," lit. "little bird." It also may have roots in Brit. public school slang fag "a junior who does certain duties for a senior" (1785), with suggestions of "catamite," from fag
(v.). This was also used as a verb.
"He [the prefect] used to fag me to blow the chapel organ for him." ["Boy's Own Paper," 1889]
Other obsolete senses of faggot were "man hired into military service simply to fill out the ranks at muster" (1700) and "vote manufactured for party purposes" (1817). The oft-heard statement that male homosexuals were called faggots in reference to their being burned at the stake is an etymological urban legend. Burning was sometimes a punishment meted out to homosexuals in Christian Europe (on the suggestion of the Biblical fate of Sodom and Gomorah), but in England, where parliament had made homosexuality a capital offense in 1533, hanging was the method prescribed. Any use of faggot in connection with public executions had long become an English historical obscurity by the time the word began to be used for "male homosexual" in 20th century American slang, whereas the contemptuous slang word for "woman" (and the other possible sources or influences listed here) was in active use.