If your tooth is broken will the dentist pull it fill it or do a root canal?

Possibly a root canal. Or he could put a false half on it.

Dentists NEVER "glue back on" the other half. If it is a small "chip" most likely a filling will do it. A larger break will require a filling to make the tooth "tooth shaped" again and then a crown. A root canal is only needed if the tooth had large decay causing the break or if the nerve of the tooth is damaged or exposed.