Born in Elgin, Robert, also known by his initials, R.C., started his football career with Elgin City.
In 1896 he moved to Glasgow, enrolling at Glasgow University to train as a teacher. Queen’s Park became aware of his footballing prowess and quickly signed him. Within a year he was a Rangers player, where he won four League medals, two Scottish Cup medals, and was capped with Scotland.
Before arriving at Dens Park in 1910, he also played for Fulham, Hearts and Morton.
Hamilton signed for Dundee on the 16th May 1910. He was living in Elgin, and found that the travel to the west coast was taking its toll, so would prefer to play for a team closer to home. He already had a relationship with the club, having been involved in the transfer of two players, John McLachlan and Allan McRobbie, from Elgin to Dundee.
Robert made his debut in a 1-1 draw versus Hibernian. It was a great start for him, scoring Dundee’s equaliser late in the game, the result of a pass from Bellamy to McLachlan to Hamilton who “without the slightest hesitation lashed the ball past Allan.” He was nearly ever present in the 1910-1911 season, scoring 20 goals. Not bad for a player that had been thought to be past his best, according to some reports, when he arrived at Dens Park.
The form he showed gained him another cap for Scotland. He was selected to play against Wales, at St Ninians Park in a Home Championship match on the 6th March 1911. Before 16,000 spectators he scored two goals, the match ending 2-2.
Raith Rovers made enquires about the chances of taking Starks Park, in May 1912, but nothing came of it.
By the end of season 1912-1913, there were rumours that Hamilton would not be kept on for the following season, as the directors were looking to enlist some younger players.
Hamilton played his last game for Dundee on the 13th December 1913, in a bad tempered game against Airdrie. Dundee lost 3-0, having had two players sent-off. He was replaced for the following home game against Rangers by Clyde Skene.
At the start of World War 1 he enlisted with, 4th Cameron Highlanders where he gained a commission, Lieutenant Hamilton was sent to the front. Writing home he expressed his thoughts on football shutting down for the duration, he stated that players that were ineligible for the army still needed to earn a living, “their welfare and the welfare of their wives and families must be looked after.” He also said that the topic of football was “the most cherished luxury that a soldier has.”
After being demobbed he returned to work at the family net manufacturing business, whilst also becoming involved in local politics. He served Elgin council until 1937, taking on the role of Lord Provost for six years between 1931-1937.
He died in May 1948, at the age of 71.