Can the Supreme court declare a treaty unconstitutional?

A treaty is an international agreement. Obviously the US Supreme Court has no juristiction over treaty between two other countries.

The president has the explict power to sign treaties, providing they have a 2/3 majority in the senate. However most treaties the US enters into are less formal "agreements"

The treaty becomes part of US federal law, and can (like any other federal law) be subject to judicial review. On rare occasions "agreements" have been rejected by the supreme court (Reid v Covert) and in this case the US would break international law and break the treaty. (Sovereign states cannot be forced to comply with treaties that they have signed except by military action, but other countries can put pressure to encourage compliance) No full Treaty (with 2/3 support) has been rejected by the court, but there is no constitution bar to this.