These cufflinks appear to have been made for James Dean, as oil tycoon Jett Rink, for the scene in Giant where Rink prepares his speech before the dinner to celebrate the formal opening of the Jett Rink Airport.
Giant was James Dean's last film - he died before filming had even finished, on 30th September, 1955, at the age of 24. The film premièred in the U.S. on 10th October, 1956 and became a huge box office hit - in fact, Giant was the highest grossing film in Warner Brothers' history until the release of Superman in 1978. James Dean was nominated for an Oscar for Best Actor In A Leading Role, his second posthumous Oscar nomination, his first was awarded the previous year, just six months after his untimely death, for the same category for his role in East Of Eden.
According to the accompanying documents, these cufflinks were given by James Dean to William Wilt, who had worked on Giant as a stagehand.