The 6-foot-1, 299-pound Rankins starred at Louisville, where he played defensive tackle and had six sacks, as well as 13 tackles for losses last season.
The selection provides the Saints with help on a defense that ranked 31st in the NFL last season, and which struggled both to pressure quarterbacks and stop the run.
During NFL meetings in March, coach Sean Payton said the Saints, who allowed 413.4 yards and a league-worst 29.8 points per game last season, were hoping to draft a play-making defensive lineman.
