Henry Horn was born in Philadelphia, Pennsylvania. He studied law, was admitted to the bar and practiced law in Philadelphia.
Horn was elected as a Jacksonian to the Twenty-second Congress. He was an unsuccessful candidate for reelection to the Twenty-third Congress in 1832. He resumed the practice of law in Philadelphia, and served as collector of customs at Philadelphia from May 12, 1845, until August 4, 1846. He died in Flourtown, Pennsylvania, in 1862. He was interred in Woodlands Cemetery in Philadelphia.
