Yes!  There are easy solutions, the best are from the vet, they'll want to charge you for exam and shots, (if no record is available), but well worth it to make your cat better and not to spread the worms to any other cats you may have.  Also, think of what you are cleaning up when you find the dead worms remains in your living quarters.  The remains look similar to rice, but you know where they've been. 

 Yes, your cat has worms. My cat has repeatedly had tape worms. There are a few type of worms. You need to take a stool sample to the Vet. And get the proper med-pill. To rid them. Cats get worms from ingesting fleas. Even though you use flea treatment, they can still occasionally pick up a few fleas; especially if they are outdoor cats.