It's possible to get worms from your dog especially if they lick their anus and then lick you in the face.
That is if the dog already has worms to pass onto you. It's best to avoid letting your dog lick you or anyone in the face since a worm called the flea worm can be passed onto you in the event a flea worm lands in your mouth and then you swallow it.
So you can get worms from dogs but there's a very small chance that you will.
But do take precautions anyway to prevent yourself or someone else from contracting the worms from the dog and always keep the dog treated for worms to prevent them from getting worms in the first place as worms can be deadly for the dogs and could be deadly for humans as well.