Baker was born near Cleveland, Ohio and moved with his parents to Morenci, Michigan.

There he attended public schools and graduated from Adrian College and from the law department of the University of Michigan at Ann Arbor.

He was admitted to the bar in 1868 and commenced practice in Leavenworth, Kansas in 1869.

From 1893 to 1895, he was a member of the State Senate and was elected as a Republican to the United States Senate.

He was the chairman of the Committee on Civil Service and Retrenchment (Fifty-sixth Congress) Afterward his term in the Senate, he resumed the practice of law in Leavenworth, where he died on June 21, 1907; he is interred in Mount Muncie Cemetery.