Born in Goshen, Indiana, Baker received a Bachelor of Arts degree from the University of Michigan in 1882 and read law to enter the bar in 1884.

[1] Baker was nominated by President Theodore Roosevelt on December 11, 1901, to a joint seat on the United States Court of Appeals for the Seventh Circuit and the United States Circuit Courts for the Seventh Circuit vacated by Judge William Allen Woods.

He was confirmed by the United States Senate on January 21, 1902, and received his commission the same day.

Following the retirement of Justice William R. Day, Judge Baker was on Warren G. Harding‘s shortlist to replace him on the Supreme Court,[2] but the seat ultimately went to Pierce Butler.

His service terminated on March 15, 1924, due to his death in Chicago, Illinois.