The U.S. troops are in Syria, and their number has just been increased. Under what international law is the deployment of U.S. troops in Syria justified?
Under contemporary international law, a military action could only be justified in three ways:
- an act of self defense is justified;
- collective self-defense, or a military action to aid an attacked ally, pursuant to a treaty of mutual defense, is justified;
- an international organization with peacekeeping functions, e.g. the United Nations (through its Security Council) or the African Union, may order military intervention.
A fourth justification for military action, counter-terrorism, is being incorporated into international law gradually. Other than these, all military actions are not justified.
The U.S. claims that its justification for military deployment in Syria is counter-terrorism against Daesh. However, this justification isn't absolutely accepted by normative international law yet. Thus, it's hard to say if American military actions in Syria are justified.
However, the international community is anarchic in nature, and there is really no one to enforce international law. There's no international police who could go into the White House and arrest the President and his cabinet members because they have violated international law. The only way to counteract against an act of invasion is either to repel the attack legitimately (which Assad is incapable of), to invoke mutual defense pacts (which Syria is not in), or to wait for the UN to direct military intervention (which is impossible, because the US has a veto in the Security Council).
Most of the contemporary US military actions abroad are unjustified or barely justified by international law, but no one can do anything about it anyway. International law is followed by most states at most occasions, but everyone do so on a good faith basis - just like how we generally follow accepted rules of ethics and conduct. No one can force you to, but doing so is generally to the interest of everyone.
The US Troop deployment in Syria has not been issued under international law. It is backed by the Authorization for Use of Military Force Against Terrorists (aka AUMF). This is a post-911 document that was originally issued for president Bush to fight against Al-Qaeda. It has since been used (controversially) as a justification for many military actions due to the vagueness and broadness of the scope defined.
...the President is authorized to use all necessary and appropriate force against those nations, organizations, or persons he determines planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001, or harbored such organizations or persons, in order to prevent any future acts of international terrorism against the United States by such nations, organizations or persons.
This is one of the foundational documents of what is frequently known as the "war on terror". In late 2016 the Obama administration published an interpretation of the AUMF that justified military action against ISIS. The current military action is support for an offensive against ISIS, so it would fall under that scope.