In the United States, can a non citizen make a citizen's arrest? Does this vary by state?
For the purposes of “citizen’s arrest” statutes, the use of the word “citizen” is interpreted broader than a citizen of a State or a national of the U.S..
It may still, however, exclude certain categories: Staff of a consular post or diplomatic mission would probably be excluded from engaging in such activity and the same probably applies for members of foreign law enforcement in their official capacities unless with special authorizations etc.
(Analogous or similar example: Frontex officers (EU boarder patrols) patrolling with local police in Member States of the EU may not carry out arrests even though they are lawfully carrying out their border patrols with local authorities and assistance of local law enforcement.)