Yes some national parks do allow what is known as dispersed camping.
When you camp in a national park for free and are dispersed camping you're basically camping with no facilities such as electricity, running water, trash service etc.
Some national parks don't allow dispersed camping while others do.
Usually they'll be a sign saying camping is not allowed or camping is allowed and if there is no sign then usually camping for free is allowed in that national forest.
But you must move at least every 14 days when camping in a national forest.