Robert Spencer may refer to:
- Robert Spencer (artist) (1879–1931), American painter
- Robert Spencer (doctor) (1889–1969), American general practitioner known for his work as an illegal abortion provider in the decades before Roe v. Wade.
- Robert Spencer, 1st Baron Spencer of Wormleighton (1570–1627), English peer
- Robert Spencer, 1st Viscount Teviot (1629–1694), English politician who sat in the House of Commons from 1660 to 1679
- Robert Spencer, 2nd Earl of Sunderland (1641–1702), English statesman and nobleman
- Robert Spencer, 4th Earl of Sunderland (1701–1729), British peer
- Robert Spencer of Spencer Combe (died 1510), landowner in Devon
- Robert B. Spencer (born 1962), American author and blogger, opponent of Islam
- Robert Cavendish Spencer (1791–1830), English officer of the Royal Navy
- Robert L. Spencer (1920–2014), Beverly Hills hairdresser and fashion designer
- J. Robert Spencer (born 1969), American Broadway actor and singer
- Lord Robert Spencer (1747–1831), British politician
- Bob Spencer (born 1957), Australian rock guitarist
- Bobbie Spencer, a character in General Hospital