Robert was the bastard son of King James V and Euphemia Elphinstone. He became Commendator of the Abbey of Holyrood as a child in 1539. He received from his half sister, Mary Queen of Scots, a tack of Orkney and Shetland in 1564 followed by a feu charter in 1565. Robert compelled Adam Bothwell, (then Bishop of Orkney), to exchange the Bishopric of Orkney for the Abbey of Holyrood in 1568. Robert was entitled the 1st Earl of Orkney in 1581.
Earl Robert was accused of treasonable dealings with Denmark and of tyrannical proceedings against the inhabitants of Orkney and Shetland in 1575. In 1571 he appointed his half-brother Laurence Bruce of Cultmalindie foud of Shetland. Bruce was an even greater tyrant than Stewart, and was the subject of a mass complaint by the Shetlanders in 1577.
Robert Stewart built the laird's house at Jarlshof in Sumburgh shortly before he died. On his death he was succeeded by his son Earl Patrick Stewart, who continued his father's reign of cruelty and terror for the islands.