I used to hear this all the time in law school, something to the effect that the US should never relinquish its sovereignty by signing the Rome Statute and subject itself to the International Criminal Court. This was at the height of the US wars in Iraq and Afghanistan, and the associated allegations of POW torture and abuse (e.g. Abu Ghraib, waterboarding, guantanamo bay, etc…). How ironic 20 years later the very same classmates that argued waterboarding wasn’t torture are the same ones that claim they can’t breathe wearing a cloth mask and mask mandates are a violation of their Constitutional Rights because of their often fabricated “medical conditions.”
Back then I’d ask my classmates to look at the other UN member countries not signatories to the Rome Statute subject to the ICC: China, Iraq, Israel, Libya, Qatar, and Yemen. Not exactly a list of countries championing human rights or state Sovereignty, the US included.
Absolute sovereignty is a very romantic notion, but the US gives up sovereignty regularly through other treaties, it is very telling the Rome Statute is where the US and others draw the line. If you are worried about violation of your US Constitutional Rights you should be significantly more concerned about the US government that in the last 20 years has created secret kills lists and conducted extra judicial killings of its own citizens including bombing citizens abroad in violation of the territorial integrity of other nations. When those charged with protecting and enforcing your Constitutional Rights are the ones violating them, I personally like the idea those bearing the most responsibility be subject to an International Court.
I don’t want to say your concern about being subject to the ICC as a civilian otherwise in contravention to your US Constitutional Rights isn’t worthy of discussion or potential concern, but it is detached from reality. Moreover, the ICC has jurisdiction over things like genocide, war crimes, and crimes against humanity it’s not exactly a “criminal court” the average citizen is likely to find themselves in violation of their Constitutional Rivhts (though perhaps you are not a civilian rather a high ranking military officer, in which case I understand your concern over an international court that prosecutes war crimes and human rights abuses).