Pinworms are one of the more common parasites that can happen with rabbits. Though usually more with rabbits living or allowed time outdoors on the ground, as they are more exposed to parasites this way. Since your bun is fairly new to you, I would suspect he came to you with them. Pretty easily treated. Your vet can administer the wormer at the appointment, then give you another dose to give 2 weeks later.
Unless it's a very heavy worm load, usually it's not going to cause any health issues. But things to watch out for would be reduced poop size, reduced appetite, and signs of belly discomfort. If you see those, then it would indicate the worms are significant enough to be causing health problems.
http://www.medirabbit.com/EN/GI_diseases/Parasitic_diseases/Pass/Pass_en.htm (pinworms in rabbits)