Small Business Payroll Protection Act of 2013 - Amends the Internal Revenue Code to require the Secretary of the Treasury to establish a registration system for payroll tax deposit agents (defined as any person that provides payroll processing or tax filing and deposit service to one or more employers). Requires such agents to: (1) submit a bond or to submit to quarterly third-party certifications, (2) make certain disclosures to their clients concerning liability for payment of employment taxes, and (3) pay penalties for failing to collect or pay over employment taxes or for attempting to evade or defeat payment of such taxes.

Requires the Secretary of the Treasury to: (1) issue a notice of confirmation of any address change for an employer making employment tax payments, and (2) send such notice to both the employer's former and new address.

Requires officers or employees of the Internal Revenue Service (IRS) who are evaluating an offer-in-compromise of a tax liability to give special consideration to an offer from a taxpayer who has been the victim of fraud.