Benjamin Jarrett was born in Sharon, Pennsylvania. He worked as a telegraph operator and later as foreman in a steel mill. He studied law, was admitted to the bar in 1907 and commenced practice in Farrell, Pennsylvania. He was city solicitor of Farrell from 1910 to 1930. He served in the Pennsylvania State Senate from 1911 to 1913. He was a member of the Pennsylvania State Workmen's Compensation Board from 1919 to 1923. He served as chairman of Mercer County, Pennsylvania, Republican committee.
Jarrett was elected as a Republican in 1937, and served until 1943, meaning he served in the Seventy-fifth, Seventy-sixth, and Seventy-seventh Congresses. He was not a candidate for renomination in 1942. He resumed the practice of law, and died, while on a visit to Zanesville, Ohio. He is buried in Oakwood Cemetery in Sharon, Pennsylvania.