Robinson was born in Westgrove, Douglas in County Cork and raised in a Protestant and Unionist family in which he was the youngest of seven children. His father, Andrew Robinson, was a middle-class stockbroker who in 1892 decided to become a clergyman in the Church of Ireland in the small Ballymoney parish,near Ballineen in West Cork. A sickly child, Robinson was educated by private tutor and at Bandon Grammar School. In August 1907, his interest in the theatre began after he went to see an Abbey production of plays by W. B. Yeats and Lady Gregory at the Cork Opera House. He published his first poem that same year. His first play, The Cross Roads was performed in the Abbey in 1909 and he became Manager of the theatre towards the end of that year. He resigned in 1914 as a result of a disastrous tour of the United States but returned in 1919. He was appointed to the board of the theatre in 1923 and continued to serve in that capacity until his death.
As a playwright, Robinson showed himself as a nationalist with plays like Patriots (1912) and Dreamers (1915). On the other hand, he belonged to a part of Irish society which was not seen as fully Irish. This division between the "pure" Catholic Irish on one side and the Anglo-Irish on the other can be seen in a play such as The Big House (1926), which depicts a burning of such a Protestant manor by Irregulars, or extreme Republicans. Robinson's most popular play was The Whiteheaded Boy (1916). His fiction includes Eight Short Stories (1919). In 1951, he published Ireland's Abbey Theatre, the first full-length history of the company.