Robert Eastham (born 1 February 1989 in Balclutha) is a New Zealand sport shooter.
Eastham represented New Zealand at the 2008 Summer Olympics in Beijing, where he competed in the men's 50 m rifle prone.
He finished only in fourteenth place by one point behind Russia's Artem Khadjibekov from the fifth attempt, for a total score of 594 targets.Eastham studied earth science at Massey University before joining the New Zealand Police.