Rodman was born June 19, 1814, in Newport, Rhode Island.[1] Young William attended the school taught by his father, a Quaker school-master.[1][2] At age 16, he moved to Providence to become a tailor's apprentice with the firm E.C. & T. Wells.[2]
Wells were the leading tailors of Providence.[2][3] Starting from about 1850, Rodman teamed with Sullivan Moulton to form the tailoring firm of Moulton and Rodman, located first in the Arcade, then at 27 Westminster Street.[3] Their customers included some of the most prominent people of Providence.[3]
Rodman was a member of the school committee and City Council before being elected to two consecutive terms as mayor from 1857 to 1859.[2] After his political career, Rodman went into the insurance business.[2]
Rodman died at his home in Providence on December 11, 1868[2] and was buried at Swan Point Cemetery.