Internet Gambling Regulation and Tax Enforcement Act of 2013 - Amends the Internal Revenue Code, with respect to the taxation of Internet gambling transactions, to:

• impose a tax on Internet gambling licensees equal to 4% of all funds deposited by their customers while located within the United States into accounts maintained by such licensees;
• impose an additional 50% tax on unauthorized bets or wagers;
• require Internet gambling licensees to keep daily records of gambling deposits and file informational returns identifying themselves and the individuals placing bets or wagers with them;
• require Internet gambling licensees to pay state and Indian tribal governments an amount equal to the monthly pro rata state and Indian tribal government online gambling tax;
• impose a tax on each Internet gambling licensee equal to 12% of all funds deposited by customers making deposits while located outside the United States into an account maintained by such licensee;
• require withholding of tax on net Internet gambling winnings and on the gross amount of winnings of nonresident aliens;
• extend the excise tax on wagers to include wagers placed within any commonwealth, territory, or possession of the United States by a U.S. citizen or resident; and
• make income earned by nonresident alien individuals and foreign corporations that are licensees of, or operating, an Internet gambling facility subject to U.S. taxation.

Directs the Secretary of the Treasury to make grants to states to carry out an American Heritage Program through state arts agencies. Allocates .5% of the tax revenues received after December 31, 2012, that are attributable to Internet gambling to the American Heritage Block Grant Fund to finance the American Heritage Program.

Amends the Social Security Act to establish the Transitional Assistance Trust Fund to finance state plans for transitional education and job training assistance to individuals who are, or were formerly, in foster care. Allocates 25% of the tax revenues received after December 31, 2012, that are attributable to Internet gambling to the Trust Fund.