if you mean "ICE agents (as sworn federal agents) are not authorized by statue to arrest people for federal crimes, like entering the US illegally" you are simply wrong.

ICE agents, specifically those in Enforcement and Removal Operations (ERO) under U.S. Immigration and Customs Enforcement (ICE), are federal law enforcement officers with statutory authority to arrest individuals for immigration violations, including criminal offenses such as illegal entry into the United States under 8 U.S.C. § 1325 and § 1327.

It is true that many immigration violations are administrative in nature but it doesn't follow that ICE are not police, nor are they not sworn to enforce all federal laws.