Alexander Johnson Irwin (March 1, 1799 – June 14, 1847) was an American merchant and Wisconsin pioneer.

Born in Greensburg, Pennsylvania, on March 1, 1799,[1] Irwin moved with his family to Detroit, Michigan Territory, and then to Green Bay in 1823.

[2] Irwin was allowed to occupy the seat while a committee investigated the election challenge.

In the federal act which established the Wisconsin Territory, it was prohibited for an existing officeholder to be elected to the Legislative Assembly.

[1] The position required trips on horseback to Saint Louis, Missouri, to deposit funds because there were no banks in Green Bay at the time.