Social Security Totalization Agreement Reform Act of 2013 - Amends title II (Old Age, Survivors and Disability Insurance) (OASDI) of the Social Security Act to provide that any agreement to establish a totalization arrangement which is entered into with another country shall enter into force with respect to the United States if (and only if): (1) the President, at least 90 calendar days before the date on which he enters into the agreement, notifies each House of Congress of his intention to enter into it, and promply thereafter publishes notice of such intention in the Federal Register; (2) he transmits the text of such agreement to each House of the Congress; and (3) a joint resolution regarding such agreement has passed both Houses of Congress and been enacted into federal law.

Sets forth procedures for the consideration of such a joint resolution.