He was born on July 18, 1823 to Sarah and Charles Hodge in Princeton, New Jersey. He was named after Charles' mentor, the first principal of Princeton Seminary, Archibald Alexander.
Hodge attended the College of New Jersey (later Princeton University) in 1841 and then Princeton Theological Seminary in 1847.
He served as a missionary in India for three years (1847–1850). He held pastorates at Lower West Nottingham, Maryland (1851–1855), Fredericksburg, Virginia (1855–1861), and Wilkes-Barre, Pennsylvania (1861–1864). In 1864 he accepted a call to the chair of systematic theology in Western Theological Seminary (later Pittsburgh Theological Seminary) in Pittsburgh, Pennsylvania. There he remained until in 1877 he was called to Princeton to be the associate of his father, Charles Hodge, in the distinguished chair of systematic theology. He took on the full responsibilities of the chair of systematic theology in 1878.
He died on November 12, 1886 in Princeton, New Jersey from "a severe cold ... which settled in his kidneys".