Not a crime *OR* The thing that politicians screaming "illegally entered the country" don't want you to know and definitely don't want you to think about:
8 U.S. Code § 1158 - Asylum
(a)Authority to apply for asylum
(1)In general
Any alien who is >>physically present in the United States or who arrives in the United States (whether or not at a designated port of arrival and including an alien who is brought to the United States after having been interdicted in international or United States waters),<< irrespective of such alien’s status, may apply for asylum in accordance with this section or, where applicable, section 1225(b) of this title.