Acid reflux does not cause high blood pressure.
More Info: Though your acid reflux may not be causing your high blood pressure, if you take certain medications, it could be your high blood pressure causing your acid reflux.
Acid Reflux May Cause Low Blood Pressure
According to one study published in April 2008 in the Gastroenterology Journal, there is actually an inverse relationship between acid reflux and high blood pressure. The study found that patients who experienced daily symptoms of acid reflux have lower blood pressure than those with infrequent or no symptoms. The findings are preliminary and may have an association with the nitric oxide link between acid reflux and low pressure. 
Acid Reflux/High Blood Pressure Connection
Though your acid reflux may not be causing your high blood pressure, if you take certain medications, it could be your high blood pressure causing your acid reflux.  High blood pressure, or hypertension, occurs when blood is pumped more forcefully than normal through the arteries. The force being exerted upon the walls of the arteries can cause damage over time.  Beta-blockers, also called beta-adrenergic antagonists, beta-adrenergic blocking agents, ore beta-antagonists, block the effects of adrenaline, which causes the heart to beat more slowly and with less force, allowing blood to flow at a normal pressure. 
Heartburn associated with acid reflux is a common side effect of beta-blockers.
Common Habits that May Associate Acid Reflux with High Blood Pressure
There are certain medical conditions, lifestyle habits, and traits that patients with acid reflux and high blood pressure have in common. For example, obesity is a risk factor for both conditions.
Alcohol Use: Having more than two drinks a day can temporarily increase your blood pressure and long-term use can lead to long-term increases. [%] Several studies have confirmed that those that consume alcohol have higher instances of GERD than those who do not. The more you drink, the higher your risk for both conditions.
Being Overweight: Obesity is one of the major risk factors for both conditions. For high blood pressure, the more you weigh the more blood your body requires forcing more pressure on the artery walls. For acid reflux, the higher your BMI the more severe your symptoms.
Family History. Both conditions tend to run in families. 
Medical Conditions. Certain medical conditions may increase the risk of both conditions including pregnancy, diabetes, and sleep apnea. 
Stress. For acid reflux, stress may make symptoms worse. In hypertension, stress can lead to dramatic, short-term increases in blood pressure. 
Tobacco Use. In acid reflux, tobacco increases the production of stomach acid, reduces saliva production, irritates the esophagus, and may impair the function of the lower esophageal sphincter—the muscle responsible for blocking stomach acids from entering the esophagus. 
Tobacco immediately raises blood pressure and can damage the lining of the artery wall.
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Inverse Association Between Gastroesophageal Reflux and Blood Pressure: Results of a Large Community Based Study
2008; Volume: 8; Print.
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Gastroesophageal Reflux Disease
 National Heart, Blood, and Lung Institute
What Is High Blood Pressure?
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 Science Daily
Mayo Clinic Researchers: Family History Identified As New Risk Factor for Heartburn
Beth Israel Deaconess Medical Center
Risk Factors for Gastroesophageal Reflux Disease (GERD)/ Heartburn
 University of Maryland Medical Center
Gastroesophageal Reflux Disease
Heartburn Tobacco Connection