To misquote someone is to incorrectly repeat the words they've said. It's unethical for a journalist to deliberately misquote the subject of an interview.
It's extremely common for people to misquote famous figures like Gandhi (who never literally said, "Be the change you wish to see in the world") and Machiavelli (who didn't exactly say, "The ends justify the means"). These examples can also be called misquotes. As with many words, Shakespeare is credited with being the first to use this combination of mis-, "wrong," and quote, "repeat or copy out exact words."