Sharia law is not recognized in the United States in the sense of it being legally binding over all citizens, but U.S. courts consider sharia when trying cases involving Muslim nations or entities. In the U.S. court system, sharia is invoked mainly in international law cases.
Sharia is a system of laws based on Islamic beliefs. It covers personal moral quandaries as well as conventional legal matters, such as marriage and domestic abuse. Sharia is part of the legal code of some Muslim nations. As such, the United States recognizes sharia when U.S. court cases involve nations where sharia is the law of the land. This is in line with established legal precedent involving the laws of foreign nations, whether or not they are religiously based.
One common example where sharia is invoked is in divorce proceedings involving Muslim immigrants who married before they arrived in the United States. Because the couple was married under sharia, the U.S.-based court must consider sharia when making its decision.
Sharia is otherwise not a part of the U.S. law code, and efforts to ban sharia in the United States are largely symbolic. Banning sharia is unconstitutional because it violates the First Amendment.