The magazine has used of a photo of the Argentine pontiff giving the thumbs up.
Inside, Italian director Ermanno Olmi talks about the pope, comparing him to "home-made bread".
It will also have a feature on young people in the Trecca quarter of Milan that the pope is set to visit on March 25.
"Rolling Stone celebrates Pope Francis, who has won over all young people with his words of attention for weakest and poorest, with his tones that are close to the common people, with a manner that is popular, no pop - the pope appears truly fit for our times".