Damar, book 1: The Blue Sword
Robin McKinley1982

Harry Crewe is an orphan girl who comes to live in Damar, the desert country shared by the Homelanders and the secretive, magical Free Hillfolk. When Corlath, the Hillfolk King, sees her for the first time, he is shaken -- for he can tell that she is something more than she appears to be. He will soon realize what Harry has never guessed: she is to become Harimad-sol, King's Rider, and carry the Blue Sword, Gonturan, which no woman has wielded since the legendary Lady Aerin bore it into battle, generations past.