He was born in Charlottetown, Prince Edward Island, the son of John Theophilus Jenkins and Jessie Esther Carson Rice, and was educated at the Ontario Agricultural College in Guelph. In 1892, he married Hannah Sarah Holroyd. Jenkins served in the province's Executive Council as a minister without portfolio from 1912 to 1915. He was speaker from 1924 to 1927. He was defeated when he ran for reelection in 1915, 1919, 1927 and 1931. Jenkins died at the Charlottetown Hospital at the age of 78.
His brother Stephen Rice also served in the provincial assembly.