The "Law of Nations" is mentioned in the Constitution. Article I gives Congress the power to enact law punishing offenses against it. To be clear here, despite the (intentional) confusion sown by transnational progressives in modern times, the Law of Nations is not the same thing as "international law." It is a finite corpus that, at the time of the founding, was understood to include only a very few offenses punishment for which was recognized as crucial to international relations and/or difficult to prosecute because they occured outside the jurisdiction of any particular nation-state.  Basically, these offenses involved interference with the safe conduct of diplomats and piracy.  Following the adoption of the Constitution, the first Congress followed through on Article I, criminalizing acts of piracy (robbery and murder on the high seas) as well as assaults on diplomats.

The mere fact that Congress makes a type of conduct illegal does not mean that conduct, thereafter, may be regarded only as a crime calling for prosecution, as opposed to an act of war justifying a military response. Military action was taken against the Barbary pirates long after piracy was criminalized in the United States — and the Mayaguez incident in 1975 prompted military action, not indictments.

Furthermore, virtually all hostile acts that occur in war could also be charged as crimes — conspiring, shooting, bombing, killing, etc. When we are at war and both sides are complying with the laws of war, combatants are priviliged to use force and are not prosecuted for doing so — other than when they commit atrocities (war crimes). But when one side is not complying with the laws of war — or is otherwise in violation of the Law of Nations — that side's operatives are unlawful combatants and not privileged to use force. In those circumstances, the fact that their acts of piracy or terrorism are criminalized under American law gives us an additional option. It does not mean we cannot treat an act of war as an act of war.