It's a phrasal verb.
To confront an unpleasant situation with resolution and assurance: had to face up or get out; finally faced up to the problem.
face up - Definitions from Dictionary.com
In your example sentence "face up" can be analyzed in two ways: either it functions as the main verb, with 'have to' as its modal or it functions as the object of the main verb 'have to'. Pick the one you know. Lastly, the verb "face" is transitive; e.g., face the music. The phrasal verb "face up" is also transitive and takes a to-prepositional phrase as its object.
All the best.