8 U.S. Code § 1325 - Improper entry by alien
Yes, crossing the border without documentation is a crime under U.S. federal law, specifically categorized as "Improper Entry by Alien". This is a misdemeanor for a first offense, which can result in fines, up to six months in prison, or both. Subsequent offenses are a felony.
(a)Improper time or place; avoidance of examination or inspection; misrepresentation and concealment of facts
Any
alien who (1) enters or attempts to enter the
United States at any time or place other than as designated by
immigration officers, or (2) eludes examination or inspection by
immigration officers, or (3) attempts to enter or obtains entry to the
United States by a willfully false or misleading representation or the willful concealment of a material fact, shall, for the first commission of any such offense, be fined under title 18 or imprisoned not more than 6 months, or both, and, for a subsequent commission of any such offense, be fined under title 18, or imprisoned not more than 2 years, or both.