Regardless of gender, King Arthur is a myth. He never existed, at least not in the context of popular culture: chivalric Knights of the Round Table, Excalibur, Merlin, Guinevere, the Holy Grail, etc. It just never happened that way, if "it" happened at all.
The best historical (as opposed to literary or legendary) THEORY is that there may - MAY - have been a Romano-Briton warlord who (briefly) united a significant portion of Britain in the 5th and 6th centuries A.D. What evidence there is suggests that the "Arthurian" kingdom (although most likely not a true "kingdom" at all) included either Wales, Cornwall and the West Country, on the one hand, or northern England and southern Scotland, on the other.
The purpose of this (supposed) unification was military and defensive in nature. In 410 A.D., Western Roman Empire, which was in its death throes, formally abandoned its province of Britannia, which it had held (with varying degrees of success) for almost 400 years. As a practical matter, Roman power in Britain had been declining for decades, and practically all Roman troops had left the province by 407.
Into this power vacuum stepped Germanic (mostly Angles, Saxons and Jutes from the northern Rhine River valley) invader-colonists, whom the remaining Romano-Britons resisted by force of arms. This is the backdrop, and the justification, for the possibility that the Arthurian legends are based in historical fact.
Regardless, Britain in the post-Empire period was a dangerous, chaotic, politically-fragmented place, and as a result, there is little historical evidence generally, and almost none at all concerning "Arthur" specifically.
Alternatively, "Arthur" may have been purely fictional, without even a grain of historical truth. His name, along with several other names in the popular Arthurian tradition, are etymologically similar to names from Welsh-Celtic mythology.
To answer your question, though, there is absolutely no reliable historical evidence for the supposition that "King Arthur" (assuming such existed) was a woman.