Rebuilding Equity Act of 2012 - Directs the Federal National Mortgage Association (Fannie Mae) and the Federal Home Loan Mortgage Corporation (Freddie Mac) (government sponsored enterprises or GSEs) each to establish a voluntary program for borrowers who qualify for the Home Affordable Refinance Program carried out by the GSEs, in which the GSE shall pay for the closing costs associated with applying for and receiving the refinancing when the borrower agrees to refinance into a fully amoritizing loan with a term of not longer than 20 years.