Joseph William Kirwan (1796 – 24 December 1849) was an Irish clergyman and educationalist, who served as the first president of Queen's College Galway.
He entered the National Seminary at St Patrick's College, Maynooth, in 1817, and was ordained to the Roman Catholic priesthood in 1822, having been awarded the degree of Doctor of Divinity (D.D.).
He was considered one of the leading candidates for appointment as Bishop of Galway when that office became vacant in 1845.
The college, one of three founded at Belfast, Cork and Galway to provide non-denominational university education in Ireland as an alternative to the Church of Ireland's Trinity College in Dublin, was not regarded with favour by a large number of prominent Catholics, among them many members of the Catholic hierarchy, who continued to press for the foundation of a specifically Catholic university.
He remained committed to the college, however, and despite failing health presided over its official opening on 30 October 1849.