5/8/2013--Introduced.Unlocking Technology Act of 2013 - Amends the prohibition under federal copyright law on the circumvention of a technological measure that controls access to a copyright-protected work to require that such prohibition apply only to circumventions carried out in order to infringe or facilitate infringement of a protected work. Declares that it shall not be a violation to: (1) circumvent a technological measure if the purpose is to engage in a use that is not an infringement of federal copyright law; or (2) use, manufacture, import, offer to the public, provide, or otherwise traffic in any technology, product, service, device, component, or part primarily designed or produced to facilitate noninfringing uses of protected works by circumventing a technological measure that effectively controls access to such work, unless the intent is to infringe or facilitate infringement of a copyright. Declares that it is not an infringement to copy or adapt the software or firmware of a user-purchased mobile communications device for the sole purpose of enabling the device to connect to a wireless communications network if: (1) the copying or adapting is initiated by, or with the consent of, the owner of that device or the owner's agent; (2) the owner or agent is in legal possession of the device; and (3) the owner has the consent of, or an agreement with, the authorized operator of such wireless communications network to make use of its network. (Thus allowing the "unlocking" of mobile devices without requiring an owner to obtain the consent of the initial carrier network before switching to a new carrier.) Directs the President to ensure that applicable bilateral and multilateral trade agreements are modified to be consistent with this Act.