Non-citizens do have rights under the Constitution, so long as they are in the United States. The 14th Amendment says that "nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws." Notice it merely says "person" and not "citizen."
Of course, this only applies to non-citizen who are in the United States ("within its jurisdiction"). It would not apply to, for example, Assad, who is in Syria.