I'm asking in general and also specifically in the example I'm going to show. In my country, international treaties have constitutional level since 1994, which means a violation of an international treaty is a violation of the constitution. For example, Argentina signed the declaration of human rights, so if a law violates a human right here, it's violating the constitution. How is this in United States? Does violating an international treaty have any legal consequence in United States?
For the US, violating the obligations of a treaty (for the purposes of international law) is not the same as a violation of the US constitution (for the purposes of domestic US law). The US Constitution is higher than treaties, and if a treaty is in conflict with the constitution, courts will rule the treaty null and void for the purposes of US law. See the Supreme Court decision in Reid v. Covert (1957). In addition, treaties do not have a privileged position over regular federal law, and simple acts of Congress can amend or repeal treaties for the purposes of US law. See the Supreme Court decision in the Head Money Cases (1884). In these cases, other countries may still regard the US to still be bound by the obligations of the treaty, even though the US may no longer be following the domestic law obligations, and thus the US may be "violating" the treaty from the perspective of international law.
Even if a treaty has not been ruled unconstitutional and has not been amended by Congress, a violation of it might still not be a violation of US law. For example, Article 33 of the Refugee Convention (which is binding on the US because it's a party to the Refugee Protocol) prevents countries from returning refugees to a country where they are persecuted. But the US government has taken the position that this treaty provision is "not self-executing" and does not by itself impose domestic legal obligations without separate domestic legislation (though others disagree). This Congressional Research Service report goes into detail about the issues surrounding the impact of treaties on US law.