Can poor circulation to the brain cause acute headaches?

Not usually: Usually poor circulation does not cause heaches.

Hard to say: Normally no, but poor circulation to the brain can result in less oxygen flow to the brain and possibly more pressure buildup. Headaches have many causes. I would see a doctor and provide a history of your headaches and get a thorough exam and whatever testing might be needed to rule out more serious issues.

Not at age 37: I do see headaches in the elderly caused by prior strokes, and tia's, and these are secondary to a combination of vasodilation in nearby normal vessels and chemical triggers due to ischemic tissue associated with decreased blood flow. Some of these events can sort of mimic migraine, but are due to an alternative cause. So, yes it does occur, but only under restricted circumstances.

Anything: Your headaches could be coming from tension, eye strain, tooth grinding, dehydration, lack of sleep/poor sleep, skipping meals, stress, sleep apnea/snoring, or chronic sinus problems.

Hard to say for sure: If you are not getting enough blood to your brain, your body will increase the blood pressure to compensate for the lack of oxygen. This increase in pressure may lead to some acute pain though not common.