Debbie,
If you mean a first-line treatment to be taken at home when a Migraine occurs, morphine would be an unusual choice.
The usual first-line treatment is Migraine abortive medications that work in the brain to stop the Migrainous process, thus relieving the symptoms. The most commonly used Migraine abortives are the triptans -- Imitrex, Maxalt, Zomig, etc.
You can find more information about the types of medications used for Migraine in Preventive, Abortive, and Rescue Medications - What's the Difference?
Hope this answers your question,
Teri