Veterans Back to Work Act of 2012 - Amends the Internal Revenue Code to: (1) extend through 2013 the work opportunity tax credit for hiring qualified veterans (veterans receiving compensation for a service-connected disability and other federal assistance), and (2) allow employers who hire qualified veterans an exemption through 2013 from employment and railroad retirement taxes. Appropriates amounts to the Social Security Old-Age and Survivors Trust Fund and the Federal Disability Insurance Trust Fund to cover any revenue loss to such Funds resulting from this Act.