Robert Jephson (1736 – 31 May 1803) was an Irish dramatist and politician.
He was born in Ireland. After serving for some years in the British army, he retired with the rank of captain, and lived in England where he was the friend of David Garrick, Joshua Reynolds, Oliver Goldsmith, Samuel Johnson, Edmund Burke, Charles Burney and Charles Townshend. His appointment as master of the horse to the lord-lieutenant of Ireland took him back to Dublin.
He published, in the Mercury newspaper, a series of articles in defence of the lord-lieutenant's administration which were afterwards collected and issued in book form under the title of The Bachelor, or Speculations of Jeoffry Wagstaffe. A pension of £300, later doubled, was granted him, and he held his appointment under twelve succeeding viceroys.
From 1775 he took up writing plays. Among others, his tragedy Braganza was successfully performed at Drury Lane in 1775, Conspiracy in 1796, The Law of Lombardy in 1779, and The Count of Narbonne at Covent Garden in 1781, adapted from Horace Walpole's The Castle of Otranto. In 1794 he published an heroic poem Roman Portraits, and The Confessions of Jacques Baptiste Couteau, a satire on the excesses of the French Revolution. Jephson entered the Irish House of Commons in 1773 and sat for St Johnstown (County Longford) until 1776. Between 1777 and 1783, he served as Member of Parliament (MP) for Old Leighlin and subsequently represented Granard from 1783 to 1790. He died at Blackrock, near Dublin.