Robert Walker Watson studied at University College, London, qualifying as a licentiate of the Society of Apothecaries of London (LSA) in 1882 and as a member of the Royal College of Surgeons of England (MRCS) in 1883. Soon after qualifying he came to the Cape Colony, where he was licensed to practice in February 1885. He settled in Ladismith, where he served as district surgeon for his entire career. In that capacity he reported annually on local public health matters. In 1905 he became a member of the British Association for the Advancement of Science when it held its annual meeting in South Africa. He was married to Jane Sarah Edwards, but they were divorced in 1903. During 1907-1910 he obtained an irrigation loan to develop the farm Bosluiskloof, just north of the Swartberg, and in 1911 a similar loan for the farm Buffelsrivierpoort.
In 1908, and also earlier, Watson presented fossils from the Bokkeveld Group to the South African Museum in Cape Town.