Telephone Surveillance Accountability Act of 2013 - Amends the Foreign Intelligence Surveillance Act (FISA) of 1978 to prohibit a person from searching telephony metadata acquired pursuant to an order to produce any tangible thing, unless: (1) the Director of the Federal Bureau of Investigation (FBI) makes an application to a FISA court judge that includes a statement of facts showing a reasonable, articulable suspicion that the basis of the search is material and specifically relevant to an authorized investigation; and (2) the judge finds that there is such a reasonable, articulable suspicion and enters an order authorizing such search.

Defines "telephony metadata" to mean communications routing information, including session identifying information, an original or terminating telephone number, an International Mobile Subscriber Identity, an International Mobile Station Equipment Identity, a trunk identifier, a telephone calling card number, and the time or duration of a call.

Requires the Director to submit to the House and Senate intelligence committees a monthly report describing each search of telephony metadata made during the preceding month pursuant to such an order.