Short answer: yes. Unless the action sought to be done via the power of attorney is one that is prohibited by law (i.e. due to federal banking regulations or U.S. Security rules), a foreign citizen can issue a power of attorney to an American citizen to perform or undertake various legal and business actions on the maker’s behalf.
In best case circumstances, the foreign citizen issuing the power of attorney should notarize the document with a licensed USA notary; for the notarization to be proper, the notary must either see the person sign the document or the person signing must attest to the notary that the signature is his or hers.
While a power of attorney notarized in a foreign country should be enforceable within the United States, the person or entity to whom the power of attorney is presented may have issues in some circumstances with a notary clause executed overseas simply due to differences in or unfamiliarity with the language of the notary clause. But if the notary clause is based on U.S. law and signed in front of a U.S. notary, there should be no issue.
To easily create a valid POA document for any USA state (with the always accepted notary clause in place), see Standard Legal’s Power of Attorney legal forms software page.