Ratner had been under fire for a gay slur he made during a recent interview.
Academy President Tom Sherak said by resigning, Ratner did the right thing for the Academy and for himself.
"Words have meaning, and they have consequences. Brett is a good person, but his comments were unacceptable," Sherak said in a statement. "We all hope this will be an opportunity to raise awareness about the harm that is caused by reckless and insensitive remarks, regardless of the intent."