Taxpayer Bill of Rights Act of 2013 - Amends the Internal Revenue Code to require the Commissioner of the Internal Revenue Service (IRS) to ensure that IRS employees are familiar with and act in accordance with taxpayer rights, including the right to be informed, to be assisted, to be heard, to pay no more than the correct amount of tax, to an appeal, to certainty, to privacy, to confidentiality, to representation, and to a fair and just tax system.