The ICC can only unilaterally enforce its statutes against citizens of countries which are signatories to the Rome treaty (which does not include the US, Russia, or China). Otherwise, it can only begin criminal proceedings against individuals in non-member countries if they are referred to the court by the governments of those countries, but it has no way to enforce its judgements or rulings on them.

This is the reason the only people who have been tried or convicted before the ICC are African warlords or former dictators, or occasionally former Serbian generals: this is just a means for the current governments to get rid of political enemies.