Castles originated in the 9th and 10th centuries, after the fall of the Carolingian Empire resulted in its territory being divided among individual lords and princes. After the death of English King Edward the Confessor and the subsequent Norman conquest of Britain and Ireland, the first castles were built in Britain.
In about 1138 Geoffrey of Monmouth’s History of the Kings of Britain contains the earliest written mention of Tintagel in the tale of how Arthur was conceived there by Uther Pendragon, King of Britain, the result of his magically assisted seduction of Queen Igerna (Igraine), wife of Duke Gorlois of Cornwall.
However, the castle wasn’t built until 1290, over 700 years after Arthur’s death and placed there to mark his birth place.
The ancient Celts didn’t build castles, the conquering Romans built fortresses and Saxons built towns, so King Arthur never did have a castle.