Rawdon was the only son of Sir John Rawdon, 3rd Baronet and Dorothy (daughter of Sir Richard Levinge, 1st Baronet, Chief Justice of the Irish Common Pleas and his first wife, Mary Corbin).
His mother remarried Charles Cobbe, Archbishop of Dublin, and died in childbirth in 1733.
In 1750 he was elevated to the Peerage of Ireland as Baron Rawdon, of Moira in the County of Down.
They had three children: Helena "died at the Hotwell, near Bristol, of the consumption"[5] in June 1746.
They had five children: Lord Moira died in June 1793, aged 73, and was succeeded by his eldest son by his third marriage, Francis, who had already been created Baron Rawdon in his own right in 1783 and was created Marquess of Hastings in 1816.