OKLAHOMA CITY—Oklahoma is far from the border and home to fewer illegal immigrants than much of the U.S. But this heartland state has emerged as the most aggressive combatant of illegal immigration alongside Arizona, thanks to a state lawmaker who has built his political career around the issue.

Arizona sparked a nationwide controversy by approving a law last month that makes it a state crime to be in the U.S. illegally and requires police to question people they stop about their immigration status if there is reason to suspect...