Waller Thomas Burns (January 14, 1858 – November 17, 1917) was a United States federal judge.
Born in La Grange, Texas, Burns was in the U.S. Customs Service before entering private practice in Galveston, Texas from 1882 to 1888. He became counsel to the Houston & Texas Central Railroad in 1888, and was a member of the Texas State Senate from 1897 to 1901.
On April 12, 1902, Burns was nominated by President Theodore Roosevelt to a new seat on the United States District Court for the Southern District of Texas created by 32 Stat. 64, 65. He was confirmed by the United States Senate on April 24, 1902, and received his commission on April 22, 1902. Burns served in that capacity until his death, in 1917, in Laredo, Texas.