Counter-Kleptocracy Act This bill addresses prevention and elimination of corruption globally. The Department of State must (1) annually rank, using specified standards, foreign countries based on their efforts to eliminate corruption; and (2) designate an anti-corruption contact in the diplomatic mission of any country that does not meet the standards. The State Department must also evaluate whether to sanction foreign persons engaged in significant corruption (1) in countries that make de minimis or no efforts to meet the standards, or (2) connected to a designated Russian pipeline project. The President may temporarily sanction foreign persons engaging in public corruption activities (e.g. bribery). The bill makes it a federal crime for foreign officials to demand or accept bribes to influence the performance of an official act or otherwise confer an improper advantage. Officials who engage in this conduct are subject to a fine, a prison term, or both. Funds recovered by prosecuting this crime shall be deposited into a new fund in the Treasury for anti-corruption initiatives. The Department of Justice must make publicly available an accounting of property relating to foreign government corruption that is forfeited to the United States. The bill addresses issues concerning U.S. visas, including related to (1) abuse of investor visas by corrupt foreign officials or criminals, and (2) foreign individuals denied admission to the United States because of adverse foreign policy consequences. The bill also prohibits extraditions based solely on, and otherwise addresses, International Criminal Police Organization communications.