Most women with migraine can take oral contraceptives relatively safely.  This is an issue which it is worth discussing with your doctor, however, as both migraine and oral contraceptives do increase the risk of stroke very slightly.

In otherwise healthy women, this risk is so slight that the benefits of the oral contraceptives usually outweigh the risks.  However, in women with migraine who also have other factors that could increase their stroke risk, such as smoking, obesity, or high blood pressure, caution and careful discussion with your doctor is advisable. Also, when it comes to migraine and oral contraceptives, migraine with aura is more of a concern than migraine without aura.

Otherwise healthy young women with migraine with aura may still find that the benefits of the pill outweigh the small risks, but if the migraine auras are prolonged or unusual in some way, then it may be best to avoid the pill.  The same may be true for women with migraine who are older over age 35.

Other methods of birth control may be a better bet for you. The best advice is that if you are going to ask your doctor for oral contraceptives, make sure your doctor knows you have migraine; and if you have auras with your migraine describe these to your doctor.

Then make a decision together as to which method of contraception is best for you.
In any case, if a woman with migraine does start the pill, it is advisable to watch for any change in the migraine.  If for example, a woman develops migraine auras for the first time after starting the birth control pill, it may be best to stop the pill.