Born in Sheffield, New Brunswick, the son of Enoch Barker, Barker was educated at the Sunbury Grammar School and received a Bachelor of Arts degree in 1856, a Master of Arts degree in 1858, and a Bachelor of Civil Law degree in 1866 from King's College Law School (now the University of New Brunswick Faculty of Law).

He also served in the Canadian Militia with the Saint-John Light Infantry and was gazetted an ensign and soon after a lieutenant in 1864.

He was elected to the House of Commons of Canada for the electoral district of City of St. John in the 1885 by-election called after Sir Leonard Tilley was appointed Lieutenant-Governor of New Brunswick.

A member of the Church of England, he married Elizabeth Julia Lloyd in 1865.

He later married Mary Ann Black, the niece and adopted daughter of former Lieutenant-Governor of New Brunswick Robert Duncan Wilmot.