Veterans Home Loan Refinance Opportunity Act of 2013 - Amends Internal Revenue Code provisions relating to tax-exempt veterans' mortgage bonds to permit: (1) proceeds from such bonds to refinance residences of veterans (currently, bond financing limited to new mortgages); (2) an annual inflation adjustment after 2013 to the amounts of veterans' mortgage bonds that states may issue; and (3) an increase from 1.125 % to 1.50% in the amount by which interest on veterans' mortgages may exceed the yield on a bond issue.