What can I do if my tooth has broken off and I have a tooth ache can a dentist take care of this?

Yes. Dentists are the experts in providing the most appropriate care for this situation. Depending on how much tooth remains (both above and below the gumline), the dentist might either perform root canal therapy to save your tooth, or extract it. Either one will resolve your pain.
Yes. Dentists are educated and experienced in treating broken teeth and toothaches.
Absolutely. And don't wait. The sooner you are seen by a dentist the sooner your tooth ache can be resolved.