Deployed Troops Support Act of 2013 - Authorizes the Secretary of Defense (DOD) to transport to any country, on a space-available basis and without charge, supplies that have been furnished by a nonprofit organization and intended for distribution to members of the Armed Forces.

Prohibits such transportation unless the Secretary determines that: (1) such transportation is consistent with U.S. policies, (2) the supplies are suitable for transportation and in usable condition, (3) there is a legitimate need for the supplies, and (4) adequate arrangements have been made for their distribution.

Makes the nonprofit organization responsible for ensuring the suitability for transport of such supplies. Allows the supplies to be distributed by the U.S. government or a nonprofit organization.