Answer: Acid reflux DOES cause headaches.
More Info: Though not generally listed as symptom of acid reflux, research has indicated a link between headaches and the disease.
Gastrointestinal Problems Linked to Headaches
Research has indicated that those who regularly suffer from acid reflux have a higher prevalence of headaches than those who do not. In fact, this same research indicates that there is a link between a variety of gastrointestinal problems and a higher prevalence of headaches including constipation, nausea, and diarrhea. 
Association between GERD, Family History, and Headache
Research has also associated gastroesophageal reflux disease (GERD) with family history and headache. The research indicated that family history is a risk factor for GERD, and that headaches are a complication of the disease. 
Common Symptoms of Acid Reflux and GERD
Headaches are not commonly listed as a symptom of acid reflux. Symptoms that are more common include heartburn, dysphagia (difficulty swallowing), globus (lump in the throat), water brash (excess saliva), hoarseness, food satiety (feeling full following small amounts of food), chest pain, bloating, belching, nausea, wheezing, lung aspiration, chronic cough, and dyspnea (shortness of breath). 
Acid Reflux and Migraines
According to Dr. Egilius L.H. Spierings MD, a headache expert from the Harvard Medical School, the occurrence of an acid reflux episode can cause pain to make its way starting from the upper gums, then to the teeth, the cheeks and finally to the eyes, where migraines are located . 
A migraine can be either a classic migraine or a common migraine. A classic migraine is also known as a migraine with aura and is characterized by head pain with visual manifestations like scotomas, photophobia and visual scintillations. On the other hand, a common migraine or a migraine without aura is a migraine episode with head pain but without the visual manifestations. Of the migraine episodes experienced by individuals, 80% of these fall under the common migraine category. 
Migraines caused by acid reflux episodes can be remedied by addressing your acid reflux problem by taking higher doses of acid reflux medication. 
Acid Reflux Medications May Cause Headaches
H2-receptor blockers. If you are taking an over the counter acid reflux medication such as Tagamet®, Pepcid®, Axid®, or Zantac®, the headaches may not be a symptom of the acid reflux, but a side effect of the medication. H2-receptor blockers work to lower stomach acid by blocking histamine release. The side effects of H2-receptor blockers are headache, diarrhea, nausea, confusion, and drowsiness. 
Proton Pump Inhibitor. Prescription proton pump inhibitors also have headaches listed as a side effect of taking the medication. Proton pump inhibitors work to block the production of stomach acid, which in turn helps to reduce the symptoms of acid reflux. Brand name proton pump inhibitors include Prilosec®, Prevacid®, Prontoix®, Aciphex®, Nexium®, and Dexilant®. The listed side effects of these medications include headache, diarrhea, stomach pain, nausea or vomiting, and increased risk of fracture. 
How to Prevent Headaches from Acid Reflux
To prevent migraines or headaches caused by acid reflux, the acid reflux disease must be addressed. Apart from medications such as antacids, H2 blockers and proton pump inhibitors, lifestyle changes such as weight reduction, quitting smoking and eating only healthy meals must be undertaken.
 Mayo Clinic
Is there any link between migraines and gastrointestinal problems?
 Saudi Journal of Gastroenterology
Correlation of Gastroesophageal Reflux Disease with Positive Family History and Headache in Shiraz City, Southern Iran
2007, Volume: 13, No: 4, pages: 176-179
 The University of Chicago Medicine
Gastroesophageal Reflux Disease (GERD)
  Prevention
 NYU Langone Medical Center
Medications for Gastroesophageal Reflux Disease (GERD)
Glossary of Terms
Dysphagia: The medical term for difficulty swallowing, or the feeling that food is “sticking” in your throat or chest.
University of Maryland Medical Center
Dyspnea: difficult or labored respiration.
Early Satiety: feeling full sooner than normal or after eating less than usual.
Globus: is the sensation of having a lump in the throat. Also called globus hystericus.
Water Brash: regurgitation of an excessive accumulation of saliva from the lower part of the esophagus often with some acid material from the stomach.
“One of the biggest problems with Proton Pump Inhibitors is that you can become dependent on them, and if you try to stop taking them you can get a rebound of reflux. Dr Oz said that you should not take Proton Pump Inhibitors like Prilosec or Prevacid for more than four weeks.”
Dr. Oz: Most Misused OTC Drugs: Headache, Heartburn, Allergy & Multi-symptom