Kleptocracy Asset Recovery Rewards Act This bill establishes in the Department of the Treasury the Kleptocracy Asset Recovery Rewards Program. The program may provide rewards to individuals furnishing information leading to the restraining, seizure, forfeiture, or repatriation of stolen assets linked to foreign government corruption. A person is ineligible for a reward if they are an officer or employee of a federal, state, local, or foreign government and furnish such information in the course of their official duties. A person may be ineligible if Treasury reasonably believes that such person knowingly participated in certain forms of government corruption. The bill provides for the administration of the program, including reward payment and eligibility. Rewards must, to the extent possible, be paid first from any recovered assets. Treasury must obtain approval from the Department of Justice before paying a reward under this Act in a matter where there is federal criminal jurisdiction.