Does the groom have to drink at the wedding? I can't drink well, and I'm afraid I'll make jokes when I'm drunk.

There has never been a custom of letting the groom drink. If you can symbolically drink less active atmosphere, it is not called drinking, it is just a matter of meaning. Generally, people who are more civilized and sensible will not force the groom to drink. Even if someone insists that the groom drink, it is not necessary. Such a person can ignore him.