The U.S. has zero land or maritime territory in the Arctic. The Arctic Circle (66°34′ N) cuts through Alaska, but the Arctic region—defined by the Arctic Ocean and its marginal seas—lies entirely north of Alaska's coast.
"Arctic" is often used loosely for "Far North Alaska." But legally and geographically, the U.S. is an Arctic nation by virtue of Alaska, not an owner of Arctic Ocean territory.
Canada, Denmark (Greenland), Norway, Russia have Arctic Ocean coastlines and EEZs. The U.S. does not—yet.