Robinson was born the son of a poor vicar in Keynsham, and was educated at Liverpool College and Christ's College, Cambridge of which he became a Fellow. He was ordained deacon in the Diocese of Ely in 1881, and priest in 1882, when he was Fellow. After a BA degree in 1881, he received his MA degree in 1884, was made Bachelor of Divinity (BD) in 1891, and Doctor of Divinity (DD) in 1896.
His first ecclesiastical posting was a Domestic Chaplain to Joseph Lightfoot, Bishop of Durham from 1883 to 1884, following which he was curate of Great St. Mary, Cambridge until 1886, then a Cambridge Whitehall preacher from 1886 to 1888. That year he was appointed examining chaplain to the Bishop of Bath and Wells and Vicar of All Saints' Church, Cambridge where he stayed from 1888 until 1892. He was also a Dean of Christ?s College, Cambridge from 1884 to 1890. In 1893 he was appointed Norrisian professor of Divinity at Cambridge university, serving as such until 1899, during which he was also a Prebendary of Wells Cathedral. He served as rector of St Margaret's, Westminster 1899-1900, and was appointed a Canon of Westminster in 1899, serving until his appointment as dean.
In January 1902 he was appointed a Chaplain-in-Ordinary to King Edward VII. The Dean of Westminster, George Granville Bradley, was severely ill throughout most of 1902, but wanted to stay in the position until the coronation of the King in August. Bradley resigned the following month, and the King appointed Robinson Dean of Westminster in early October, followed by a formal installation in Westminster Abbey on 28 October 1902. He served at Westminster until he was appointed Dean of Wells in 1911. It has been suggested that the move to Wells was arranged to avoid friction in the run-up to the coronation of George V.
Robinson was Lord High Almoner from 1906 to 1933.
As Dean of Wells Robinson enjoyed close links with Downside Abbey. He also critically explored the origins of the Glastonbury legends to which the Glastonbury Festival had revived attention. A renowned scholar in patristics (he was particularly known for his work on the Lausiac History and for having been the first person to translate into English the newly discovered work by Irenaeus The Demonstration of the Apostolic Preaching), Armitage Robinson was a participant in the bilateral Anglican-Roman Catholic Malines Conversations.
He was appointed Knight Commander of the Royal Victorian Order (KCVO) in 1932, and died on 7 May 1933.