It's the first time the staunchly liberal rock-music bible has featured a Roman Catholic pontiff on its cover, which is typically graced by pop stars and movie idols.
"Pope Francis: the times they are a-changin'," reads the cover headline that borrows the title of Bob Dylan's classic early 1960s anthem.
The Argentine-born Pope, who took office in March last year, has previously been Time magazine's Person of the Year. He also made the cover of The Advocate, the respected US gay rights magazine.
In an accompanying 8,000-word profile, seen on its website on Wednesday, Rolling Stone hailed the pontiff's relaxed style and his less aggressive stance on such hot-button issues as homosexuality compared to his two predecessors.
In a statement, Rolling Stone's editors said they had been struck by his seeming effort to play down "culture war issues" and his willingness to talk "about real world economic issues in starkly moral terms."
"His tone is a breath of fresh air, but his message is a wake-up call," they said.
Roman Catholics make up the biggest Christian denomination in the United States, but polls indicate lay Catholics don't all share the national church leadership's hardline stance on abortion, contraception and gay marriage.