What can my teenager take for migraines?

Varies. First of all, be sure they are migraines. If so, many treatments are available for this. A pediatric neurologist or neurodevelopmentalist is your best bet to help with treatemnt. By the way, diet and sleep problems can impact migraines significantly.
NSAID's. Antiinflammatories like ibuprofen, Naproxen and others are the first line of treatment for migraine headaches, even in adults. Because of your question, i think you are aware that triptan drugs like imitrex, (sumatriptan) Maxalt and others are not indicated at his age.