The South Dakota State Jackrabbits football program represents South Dakota State University in American football. This article covers the history of the program in the first two decades. Prior to 1904, the school was known as the South Dakota Agricultural College. In 1904, the school was renamed South Dakota State College of Agriculture and Mechanic Arts. The team played its home games at Brookings, South Dakota.

The 1904 college football season had no clear-cut champion, with the Official NCAA Division I Football Records Book listing Michigan, Minnesota, and Penn as having been selected national champions.