Sports Gaming Opportunity Act of 2012 - Amends the federal judicial code to exempt a lottery, sweepstakes, or other betting, gambling, or wagering scheme authorized by a state by a statute enacted on or after January 1, 2012, and in effect not later than January 1, 2016, from the prohibition against a governmental entity, or a person acting pursuant to the law or compact of a governmental entity, sponsoring, operating, advertising, or promoting sports gambling.