The move comes after an independent review concluded the magazine failed to follow basic journalistic safeguards before publishing.
The November article described a gang rape at a University of Virginia (UVA) fraternity house in 2012.
A four-month police investigation found no evidence that the incident occurred.
However, police chief Timothy Longo has said that did not mean "something terrible didn't happen" to the student known as Jackie.
In a statement, UVA's chapter of Phi Kappa Psi said they would "pursue all available legal action against the magazine".
The chapter said its members were ostracised and the fraternity house was vandalised as a result of the article, which was read by millions.
The Columbia School of Journalism report, commissioned by Rolling Stone, described the article as "a story of journalistic failure".
Written by journalist Sabrina Erdely, the 9,000-word article A Rape on Campus relied on Jackie as the sole source to tell the story of an alleged rape at the Phi Kappa Psi fraternity house.
Subsequent investigations by other reporters and Ms Erdely herself identified errors in the reporting of the piece.
Rolling Stone has apologised and officially retracted "A Rape on Campus" after the review.
Managing Editor Will Dana apologised to readers and "all of those who were damaged by our story and the ensuing fallout".
The Columbia School of Journalism report said the magazine failed to use "basic, even routine journalistic practice" to verify the details after Ms Erdely failed to contact the alleged attackers.
"The failure encompassed reporting, editing, editorial supervision and fact-checking", and there were "systematic failures" at the magazine, the report said.
The report went on to suggest that the article had undermined work to stop sexual violence as it "spread the idea that many women invent rape allegations".
During a press conference on Monday, Steven Coll, one of the authors of the report, said Rolling Stone had hid behind sensitivity to Jackie to explain their lapses in reporting.
"We do disagree with any suggestion that this is Jackie's fault," Mr Coll added.
Mr Dana described the report as "painful reading", and said the magazine was committing itself to a series of recommendations in the report, but said no-one would be fired for their involvement in the story.
He apologised to all those affected by the story, "including members of the Phi Kappa Psi fraternity and UVA administrators and students".
Columbia said that Jackie had declined to answer questions for the report and that her lawyer said it "is in her best interest to remain silent at this time".
The fraternity at the centre of a discredited Rolling Stone article about a campus rape has threatened to sue the magazine for its "reckless" reporting.