No.
Federal Land, yes. National Park, no.
The federal government manages 640 million acres. This land is held in trust for the American people, primarily managed by 4 agencies:
the National Park Service (NPS) - 84 million acres, 3.7% of the land
the Bureau of Land Management (BLM) -248 million acres,10.5% of all land
the United States Forest Service (USFS) =193 million acres, 8.5% of the land
the United States Fish and Wildlife Service (USFWS)=95 million acres (3.9% of land) + 760 million acres of submerged lands and waters
A small share of federal land is managed by the Department of Defense and other agencies.
The remaining 199 million acres of public land is managed by state and local agencies =199 million acres, 8.7% of the country’s land.