They 'swore' (an oath of) allegiance to the United States of America. [=they formally promised that they would be loyal to the United States of America]
He 'swore us to secrecy/silence'. [=he made us promise not to tell anyone his secret]
He was so disgusted by the election results that he 'swore off' politics for good.
(..) fulfilled their pledge. Who shall call them from the grey twilight? The forgotten people. The heir of him to whom the oath they swore. From the north shall he come. Need shall drive him. He shall pass the door to the Paths of the Dead. The very warmth of my blood (..)2003 The Lord of the Rings: The Return of the King
(..) ...and no more despair. What kind of army would linger in such a place? One that is cursed. Long ago, the Men of the Mountains swore an oath... ...to the last king of Gondor... ...to come to his aid... ...to fight. But when the time came... ...when Gondor's need was dire... (..)2003 The Lord of the Rings: The Return of the King