Yes. Migraine can cause bloodshot eyes. But friend, I suggest you to see the doctor first because your headache may be caused by other reasons. You must have your body checked. And bloodshot eyes may be caused by several reasons thought migraine is one of the causes. If you stay up too late recently and don't get enough sleep, it may lead to bloodshot eyes too. Or you just infected your eyes by rubbing them with your dirty hands. It may lead to pink eye which contain the symptom of bloodshot eyes.
I am sorry to tell you that people will get bloodshot eyes with migraines. In your brain, the blood vessels may spasms when the headache happens. This will increase your blood pressure. And it will further affect your eyes. It will lead to high eye pressure. At this moment, the bloodshot eyes appear due to high eye pressure. You can take aspirin and then to take a nap. Vitamin C can help you with this too. But if the symptom still exists, I suggest you to take a thorough eye examination and then find some treatment to get rid of this situation. Other situations such as lack of sleep, smoke in the eyes, or some objects in the eyes may cause bloodshot eyes too. Hope these can be helped.