MajorNelson has announced that Treyarch’s Call of Duty 3 is now available on Xbox One via backwards compatibility.
— \\ Larry Hryb \\ (@majornelson) September 22, 2016
You can visit the Xbox One store now to find Call of Duty 3. If you already own the game, then it should show up as a free download on your Xbox One. For those that own a disc version of the game, you should be able to insert your disc into the Xbox One and play Call of Duty 3 now.
Thus far, Call of Duty 2, Call of Duty 3, and Call of Duty: Black Ops 1 are the only Call of Duty games available via Xbox One backwards compatibility.