William C. Arnold was born in Luthersburg, Pennsylvania. He attended the public schools and Phillips Academy in Andover, Massachusetts. He studied law, was admitted to the bar in Clearfield County, Pennsylvania, and practiced in Curwensville and Du Bois, Clearfield County, Pennsylvania.
Arnold was elected as a Republican to the Fifty-fourth and Fifty-fifth Congresses. He was an unsuccessful candidate for reelection in 1898. He resumed the practice of law in Clearfield County and died in Muskegon, Michigan, while on a business trip. Interment in Oak Hill Cemetery in Curwensville.