"Does the United States of America currently have a Citizenship-through-Investment Program?"

The concise answer to this question is: No. Although in the United States, it is not possible to receive Citizenship merely through investing capital therein. However, one could argue that the EB-5 visa is a "path to citizenship by investment." Through participation in the EB-5 Immigrant Investor program the foreign immigrant can receive Lawful Permanent Residence (LPR) if their visa application is approved and they are admitted lawfully to the United States. Once in the "LPR" status the foreign investor may be able to naturalize to American Citizenship upon meeting the eligibility criteria for naturalization and fulfilling the requisite statutory physical presence period as stipulated under the relevant sections of the American Immigration and Nationality Act (INA).