you said George C. Scott or Marlon Brando, you're off by 35 years.
Dudley Nichols turned down his 1935 Best Screenplay Oscar for
The Informer in protest of the Academy's attempts to act as a trade
When the Academy got out of the labor organizing business two years later,
Nichols finally accepted his award.
He received three subsequent Oscar nominations, for The Long Voyage Home (1940),
Tin Star (1943) and Air Force (1957), although he was overlooked for
his work on the Best Picture nominees Stagecoach (1939) and The Bells of St. Mary's (1945).
For rookie Oscar quiz-takers, Scott famously declined his nominations in 1961 for The Hustler and in 1970 for Patton, claiming that he had no respect for the Academy (he did not decline other awards such as the Emmy he won for the Hallmark Hall of Fame telecast of The Price he won the same year that he declined the Patton Oscar, nor did he turn down his first Oscar nomination for Anatomy of a Murder in 1959) and that the Oscar ceremony was "a two-hour meat parade, a public display with contrived suspense for economic reasons." He didn't show up to collect his Patton Oscar when he was declared the winner but he did sit in the audience of the 1982 meat parade, refusing to take interviews when he walked the red carpet to enter the theatre.
Brando made world headlines by sending a woman in full Indian regalia calling herself Sacheen Littlefeather to read a 15-page speech turning down his Oscar for The Godfather because of Hollywood's depiction of Native Americans. The network only allowed Littlefeather (who it was later revealed was an actress named Maria Cruz) to make a short on-air speech, which she performed with compassion and graciousness. Brando's rejection of the award (and the fact that he failed to show up to do it himself) was a predictably controversial act which resulted in a feud with The Godfather producers that ended with his refusing to reprise his role of Vito Corleone in a cameo appearance at the end of The Godfather II.