Sir Robert Shaw, 1st Baronet (29 January 1774 – 10 March 1849) was a Tory UK Member of Parliament who represented Dublin City from 1804 to 1826.
Sir Robert's great-great-grandfather, William Shaw, had gone to Ireland and fought for King William at the Battle of the Boyne in 1689, and was rewarded by the grant of land there. William's great-grandson, Robert Shaw sr., moved to Dublin in the mid-18th century, prospered as a merchant and became Accountant General of the Post Office. In 1785 he acquired Terenure House, an estate of 35 acres (140,000 m2). His eldest son, Robert, was born in 1774.
On 7 January 1796 Robert jr. married Maria, daughter and heiress of Abraham Wilkinson, and as a dowry received £10,000 together with a 110-acre (0.45 km2) estate, Bushy Park (possibly named after Bushy Park in Teddington) which adjoined Terenure House. Six months later he succeeded his father to the Terenure estate, which he sold in 1806, establishing Bushy Park House as the family seat (which was then occupied by members of the Shaw family until 1951).
Between 1799 and 1800, Shaw served in the Irish House of Commons for Bannow. In a by-election on 31 March 1804 Shaw replaced the former Tory MP John Claudius Beresford. Shaw retained the seat until he retired, at the dissolution of Parliament, in 1826. He was also appointed High Sheriff of County Dublin for 1806–07. He was created a baronet (i.e. becoming Sir Robert) on 17 August 1821, being formally invested by George IV when he visited Ireland in 1822.