While the film itself is a classic Western, the song he sings, "A Fistful of Dollars", is actually an instrumental piece composed by Ennio Morricone. The song plays during the iconic scene where Eastwood's character, "The Man with No Name," walks into a town with a coffin in tow.
It's a bit of a trick question, as Eastwood doesn't actually *sing* in the movie, but the song is so closely associated with him and his character that it's considered one of his signature moments.