10 USC 504 - Persons not qualified

(a) Insanity, Desertion, Felons, Etc.— 
No person who is insane, intoxicated, or a deserter from an armed force, or who has been convicted of a felony, may be enlisted in any armed force. However, the Secretary concerned may authorize exceptions, in meritorious cases, for the enlistment of deserters and persons convicted of felonies.
(b) Citizenship or Residency.— 

(1) A person may be enlisted in any armed force only if the person is one of the following:
(A) A national of the United States, as defined in section 101(a)(22) of the Immigration and Nationality Act (8 U.S.C. 1101 (a)(22)).

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(B) An alien who is lawfully admitted for permanent residence, as defined in section 101(a)(20) of the Immigration and Nationality Act (8 U.S.C. 1101 (a)(20)).
(C) A person described in section 341 of one of the following compacts:
(i) The Compact of Free Association between the Federated States of Micronesia and the United States (section 201(a) of Public Law 108188 (117 Stat. 2784; 48 U.S.C. 1921 note )).
(ii) The Compact of Free Association between the Republic of the Marshall Islands and the United States (section 201(b) of Public Law 108188 (117 Stat. 2823; 48 U.S.C. 1921 note )).
(iii) The Compact of Free Association between Palau and the United States (section 201 of Public Law 99658 (100 Stat. 3678; 48 U.S.C. 1931 note )).
(2) Notwithstanding paragraph (1), the Secretary concerned may authorize the enlistment of a person not described in paragraph (1) if the Secretary determines that such enlistment is vital to the national interest.