The US has them as well, just they didn't require being actual castles by the time the new world was discovered.
Castillo de San Marcos Fort, St. Augustine, FL
It has a sister down in the Keys as well..
Fort Jefferson FL, Keys
In the US though most older forts were made of wood as they mainly were put up in defense of Indians and not full scale invasions from other military forces. The two Spanish era forts are exceptions and around FL, you can find smaller examples of old watch towers or stations built of stone or rock that are still standing today.