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.
(..) just painting during my absence. Oh. You think I had something to do with the robbery? Didn't you? You little beast. Three - No. Four years ago I swore to you that I was retired. I've been faithful to you ever since. In your fashion. What the hell does that mean? (..)1975 The Return of the Pink Panther