Wireless Device Independence Act of 2013 - Amends the Digital Millennium Copyright Act (DMCA) with respect the prohibition on the circumvention of technological measures that control access to a copyright-protected work. Expands the exceptions to such prohibition to allow the user of a computer program (in the form of firmware or software) that enables a wireless telephone handset or other wireless device that can connect to the Internet, and that is originally acquired from the operator of a wireless telecommunications network or retailer, to connect to a different wireless telecommunications network (a practice commonly referred to as "unlocking" the underlying device) if: (1) the user legally owns a copy of the computer program, (2) the use of the program is solely for connecting to such wireless telecommunications network, and (3) the access to such network is authorized by the network operator. (The Librarian of Congress had previously provided an administrative exemption from the DMCA prohibition to permit the unlocking of mobile wireless devices but the exemption was not renewed after a rulemaking the DMCA requires to be conducted every three years.)