Boko Haram Terrorist Designation Act of 2013 - Expresses the sense of Congress that Boko Haram has met the criteria for designation as a foreign terrorist organization, and the Secretary of State should so designate Boko Haram.

Provides that if the Secretary does not designate Boko Haram as a foreign terrorist organization within 60 days the Secretary shall submit a report to Congress that contains the reasons therefor.

Directs the President, in concert with applicable Nigerian law, to subject to sanctions any person in the United States or subject to U.S. jurisdiction who knowingly provides material support or resources to Boko Haram or its affiliates, associated groups, or agents.

Prohibits the Secretary from issuing any visa to, and directs the Secretary of Homeland Security (DHS) to deny U.S. entry to, any member or representative of Boko Haram or its affiliates, associated groups, or agents.

Requires under certain circumstances, the removal from the United States of any alien who is a member or representative of Boko Haram or its affiliates, associated groups, or agents.

Requires any U.S. financial institution that knowingly has possession of or control over funds in which Boko Haram or its affiliates, associated groups, or agents have an interest to: (1) retain possession of or control over the funds, and (2) report the funds to the Office of Foreign Assets Control of the Department of the Treasury.