Robert Aglionby Slaney (9 June 1791 – 19 May 1862) was a British barrister and Whig politician from Shropshire. He sat in the House of Commons as a Member of Parliament for the borough of Shrewsbury for most of the period from 1826 until his death in 1862.
Slaney was the eldest son of Robert Slaney (1764–1834) of Hatton Grange, Shropshire, and his wife, Mary, daughter of Thomas Mason of Shrewsbury. He was educated at Trinity College, Cambridge, and was called to the bar in 1817 at Lincoln's Inn.
He was first elected at the 1826 general election, and was re-elected at the next three general elections, until his defeat at the 1835 general election by the Conservative Party candidate John Cressett-Pelham. He was re-elected in 1837, but did not stand in 1841, when the seat was won by Benjamin Disraeli. He won the seat again in 1847, but did not stand in 1852. He was High Sheriff of Shropshire in 1854.
Slaney was returned again at the 1857 general election, re-elected in 1859, and held the seat until his death, aged 70.