Augustus Drum was born in Greensburg, Pennsylvania. He received private instruction and attended Greensburg Academy. He graduated from Jefferson College (now Washington and Jefferson College) in Canonsburg, Pennsylvania. He studied law, was admitted to the bar in 1836 and commenced practice in Greensburg. He was a member of the Pennsylvania State Senate in 1852 and 1853. He also held several local offices.
Drum was elected as a Democrat to the Thirty-third Congress. He was an unsuccessful candidate for reelection in 1854. He resumed the practice of law in Greensburg and died there in 1858. Interment in St. Clair Cemetery.