Acid reflux CAN cause a sore throat.
More Info: If stomach acids reflux through the esophagus and into the larynx, it can cause a condition known as laryngopharyngeal reflux, which can cause a chronic sore throat. 
What Is the Laryngeal Pharynx?
The pharynx is the part of the throat just below the mouth and nasal cavity. It functions in both a digestive and respiratory capacity. It is separated into three parts, the nasal pharynx, the oral pharynx, and the laryngeal pharynx. The laryngeal pharynx is connected to the esophagus, the tube that delivers food from the throat to the stomach. 
Digestion and Acid Reflux
After swallowing food, it moves from your mouth to the pharynx, passing through the esophagus, and into the stomach, where acidic digestive juices begin their work of breaking down the food for use by the body. The esophagus contains ring-like muscles on either end that open and close to allow food to flow through and prevent digestive juices from refluxing. The lower esophageal sphincter is located between the stomach and the esophagus. The upper esophageal sphincter is located between the esophagus and the laryngeal pharynx. When these work incorrectly, acid reflux can occur. 
Commonly acid reflux affects the esophagus, but when it passes through the esophagus and into the laryngeal pharynx, a condition called laryngopharyngeal reflux (LPR) can occur. This can result in a cough, repetitive throat clearing, and voice changes. 
The larynx is not equipped to handle gastric acid and as few as three episodes can lead to damage. 
As many as 65% of people with laryngopharyngeal reflux do not experience symptoms of heartburn and are unaware that they may possibly have GERD. If a chronic sore throat is caused by GERD, controlling the GERD is usually effective. If treatment is unsuccessful, it may be another disorder known as esophagopharyngeal reflux. 
Esophagopharyngeal Reflux (EPR)
Those who don’t respond to typical therapies for laryngopharyngeal reflux are sometimes found to have EPR. Rather than gastric juices entering the larynx, EPR is the regurgitation of ingested foods from the upper portion of the esophagus back into the larynx. This can cause throat clearing, cough, and excessive mucous. 
The Dreaded Diagnosis of Laryngopharyngeal Reflux Disease
 Encyclopedia Britannica
Pictures of the Esophagus
  Gastroenterology and Hepatology; Joel E Richter, MD
Advances in GERD: Current developments in the management of acid-related GI disorders
2009; Volume: 5; No: 7; Pages: 485-487
 Allergy and Asthma Proceedings; Franco RA Jr.
2006; Volume: 27; No: 1; Pages: 21-26