Rhodes Semmes Baker was born on May 30, 1874, in Duck Hill, Montgomery County, Mississippi.

He was an American attorney. His family moved to Texas in 1884 and settled in San Angelo, where his father operated a hardware store and served as Commissioner of the General Land Office from 1895 to 1899. Baker, while working in his father's business, educated himself in hopes of becoming an attorney. Despite having no academic coursework, he was accepted to the University of Texas in Austin. Baker not only pursued legal studies but also edited several student publications. He graduated at the top of his class in 1896, moved to Dallas, and established a successful law practice. Baker was admitted to practice before the United States Supreme Court in April 1901 and successfully argued several cases. In his most famous one, Hopkins v. Baker, he convinced the justices of the legality of a Texas state law allowing married couples to file separate tax returns, thereby reducing their tax burden. He was a member of the American Bar Association, as well as the state and local bar associations, and served as President of the University of Texas Ex-Students Association.

He was a member of the First Presbyterian Church, where he taught Bible classes for thirty-seven years, and served as President of the Young Men's Christian Association. He acquired an impressive selection of paintings, including works by George Inness, Thomas Gainsborough, Joshua Reynolds, and George Romney, and served as President of the Dallas Art Association. Austin College awarded him an honorary Ph.D. in 1924. At the time of his death, he was a partner in the law firm of Thompson, Knight, Baker, and Harris, chairman of the board of the Dallas Building and Loan Association, and a member of the board of directors of Republic National Bank.

In 1899, he married Edna Miller Rembert (1878–1955). He died on February 6, 1940, in Dallas, Texas.