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.
(..) the watcher on the walls, the shield that guards the realm of men. - I pledge my life... - Okay, that's enough. Shield that guards the realm of men. That's what you swore to be. Now I'm not a learned man, the best way of helping the most people might not be sitting in a frozen castle at (..)2015 TvShow: Game of Thrones Title: High Sparrow Season: 5 Episode 3
(..) to avenge your family. Take back the castle where you grew up. To rule the North. I wish I could fight beside you. Believe me, I do. But I swore a sacred vow at the Godswood. I pledged my life to the Night's Watch. You're as stubborn as your father. And as honorable. I can imagine no higher praise. (..)2015 TvShow: Game of Thrones Title: High Sparrow Season: 5 Episode 3