Question: are geralt and ciri betrothed?
Answer: Ciri is Geralt's adopted daughter, bound to his destiny by the Law of Surprise. The books and Netflix show detail how Geralt came to have his fate intertwined with Ciri's, and it would later be that Ciri would also become a Witcher under the tutelage of Geralt. So Geralt can be seen as her adoptive father and mentor.