Safeguarding Social Security Numbers Act of 2013 - Directs the Commissioner of Social Security to issue uniform standards for the method for: (1) truncation of Social Security account numbers in order to facilitate their protection from use in fraud or identity theft, and (2) encryption (or other method of securing) of those numbers transmitted by means of the Internet.
Applies such standards to the federal government whenever it: (1) displays a Social Security account number; and (2) transfers, records, or otherwise utilizes such a number.
Prohibits a state, a local government, or any of their officers, employees, or contractors from displaying to the general public on the Internet all or any portion of any Social Security account number, except in compliance with such truncation and encryption standards or if the number belongs to a deceased individual. Prescribes a civil monetary penalty of up to $5,000 per day for violation of this prohibition.
Directs the Attorney General to award grants to state and local governments to carry out activities to remove, redact, or truncate, in accordance with the uniform standards, all Social Security account numbers on forms and records of their executive, legislative, and judicial agencies that would be displayed to the general public on the Internet in violation of this Act.