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.
(..) If she had a sword, she'd taken my kingdom. "Bring me the king's daughter", and you let her slip right through your tiny little fingers. How? You swore that you would protect me! You swore! Yet there's no one I can trust. No one, there's no loyalty, no loyalty! (..)2012 Snow White and the Huntsman