Thorfinn Torf-Einarsson also known as Thorfinn Skull-splitter was a 10th-century Earl of Orkney. He appears in the Orkneyinga saga and briefly in St Olaf's Saga, as incorporated into the Heimskringla. These stories were first written down in Iceland in the early 13th century and much of the information they contain is "hard to corroborate".

Earl of Orkney, historically Jarl of Orkney, is a title of nobility encompassing the archipelagoes of Orkney and Shetland, which comprise the Northern Isles of Scotland. Originally founded by Norse invaders, the status of the rulers of the Northern Isles as Norwegian vassals was formalised in 1195. Although the Old Norse term jarl is etymologically related to "earl", and the jarls were succeeded by earls in the late 15th century, a Norwegian jarl is not the same thing. In the Norse context the distinction between jarls and kings did not become significant until the late 11th century and the early jarls would therefore have had considerable independence of action until that time. The position of Jarl of Orkney was eventually the most senior rank in medieval Norway except for the king himself.