Build America Bonds Act of 2012 - Amends the Internal Revenue Code to: (1) make permanent the issuance authority for Build America Bonds and the authority for payments to issuers of such bonds; (2) make phased reductions in the credit percentage to bondholders and the percentage of payments to issuers of such bonds; (3) allow refundings of currently issued bonds; (4) allow the use of Build America bonds to fund capital expenditures for levees and flood control projects; and (5) deny a tax deduction to major integrated oil companies for income attributable to the production, refining, processing, transportation, or distribution of oil, gas, or any primary product thereof.