Was there a female knight of the round table?

No. Knights were (and are) by definition male. A knight's wife assumes the title of "lady". The female equivalent of a knighthood is a "dame".
I am unaware of any female Knight of the Round Table, but there is no reason why one should not have existed. There was certainly a famous female knight in the Matter of France, named Bradamante; these works were contemporary with the medieval literature on the Round Table and dealt with Charlemagne and his people.
There is a link to a related question on female knights below, where the subject is dealt with in more detail.
There is also a link to an article on Bradamante.