No, he is single and has said he is not gay, but I doubt many believe the not gay part. ;)
Graham has never been married and when asked by Robert Draper of the New York Times said “I know it’s really gonna upset a lot of gay men—I’m sure hundreds of ’em are gonna be jumping off the Golden Gate Bridge—but I ain’t available I ain’t gay. Sorry.”
^ Draper, Robert (June 28, 2010). “Lindsey Graham, This Year’s Maverick”. The New York Times Magazine. pp. MM22.
Oscar Wilde had a wife and two kids. Grahamnesty is a lifelong bachelor. G-d, I love irony.