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.
(..) - Police? How many? - All of them, l think. Go! I'll finish here. I'll take care of the police. - Wait, you swore. . . Trust me. Hey you at the window, drop your weapon and place your hands on top of your head. That's a damn mini-gun! (..)1991 Terminator 2: Judgment Day