He was the second son of John Stratford, 1st Earl of Aldborough and his wife Martha O'Neale, daughter of the Venerable Benjamin O'Neale, sometime Archdeacon of Leighlin. He was a descendant of the English Stratford family
In 1763, Stratford, stood as Member of Parliament (MP) for Baltinglass, the same constituency his father and his older brother had represented before, and held this seat until 1777. Subsequently he was returned to the Irish House of Commons for Wicklow County. From 1790, he sat again for Baltinglass until the Act of Union in 1801, when he succeeded his older brother Edward as earl.
In 1795, Stratford was appointed Governor of County Wicklow.
In April 1777, he married Elizabeth Hamilton, eldest daughter of Reverend Frederick Hamilton, Archdeacon of Raphoe and son of Lord Archibald Hamilton, and had by her three daughters. The oldest, Elizabeth, named after her mother, married John Halliday, later Tollemache, and had John Tollemache, 1st Baron Tollemache. Louisa-Martha (1748–1814), married Hon. John Rodney, a younger son of George Rodney, 1st Baron Rodney, and Emily (died 1863), married Thomas Best (died 1829).
Stratford died at Belan House in County Kildare in 1823 and lacking male issue, he was succeeded in his titles by his younger brother Benjamin. His wife died in 1845.