It's complicated.

Originally the author wanted to make Artoria male and his master a female character but was pressured to do the opposite and to make Fate an eroge. There is an alternate version of Artoria now that is male but that's not really the "canon" one for the Fate SN/UBW/HF timelines. In-canon, Artoria is female though which caused problems for her father because he wanted a male successor which is why he had her raised in the countryside by a knight. After her ascension to King however people sort of glazed over the whole female thing and mainly just focused on her being a King. In the Nasuverse it is semi-well known (at least among mages) that Artoria is a female, though sometimes magic rituals can fuck up summoning a servant and make them crazy, an animal, the opposite gender, a different class, or even a god sometimes. Things get way weirder in lore when you realize Artoria and her sister Morgan Le Fay sired Mordred…

Fate is a weird series.