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.
(..) have already done that. You have allowed this dark lord to twist your mind, until now– until now you have become the very thing you swore to destroy. Don’t lecture me, Obi-Wan. I see through the lies of the Jedi. I do not fear the dark side as you do. I have brought peace, freedom, justice... (..)2005 Star Wars: Episode III - Revenge of the Sith