William Fosgate Kirby (November 16, 1867 – July 26, 1934) was a Democratic Party politician from Arkansas who represented the state in the U.S. Senate from 1916 to 1921.

Kirby was born in Miller County, Arkansas, near Texarkana, on November 16, 1867, and attended common schools.

He was the state's attorney general from 1907 to 1909 and was elected associate justice of the Arkansas Supreme Court, serving from 1910 to 1916.

He resigned upon his election to the Senate to serve out the term of James P. Clarke, who had died in office.

He again became an associate justice of the state supreme court, serving from 1926 until his death; he died in Little Rock on July 26, 1934, and is buried in Texarkana.