The 1960 Texas Longhorns football team was an American football team that represented the University of Texas (now known as the University of Texas at Austin) as a member of the Southwest Conference (SWC) during the 1960 college football season. In their fourth year under head coach Darrell Royal, the Longhorns compiled an overall record of 7âÂÂ3âÂÂ1, with a mark of 5âÂÂ2 in conference play, and finished tied for third in the SWC. Texas concluded their season with a tie against Alabama in the Bluebonnet Bowl.