swear (someone) to secrecy

Translations
поклясться (кому-то) в хранении тайны
He swore me to secrecy about the surprise party.
Он поклялся мне хранить тайну о вечеринке-сюрпризе.
Definitions
To make someone promise not to tell anyone else about something, usually by asking them to give their word or make an oath to keep it confidential.