High blood pressure CAN cause tinnitus.
More Info: Though high blood pressure can cause tinnitus, it is very seldom the cause of it.
How Common Is Tinnitus?
Tinnitus is the medical term for the perception of sound within the ear when no external source is present. Temporary tinnitus is a common condition that affects fifty-percent of the population at some point. This temporary condition can be caused by such things as exposure to loud noises such as a concert that will cause a ringing sensation even after the music has stopped. Up to twenty percent of the population experiences chronic tinnitus. 
What Causes Chronic Tinnitus?
When tinnitus becomes an ongoing condition, it is often a symptom of another problem. Generally, conditions that cause tinnitus are not serious and are caused by ear related problems including chronic exposure to loud noise, ear infections, a blocked ear canal, abnormal growth of bone in the middle ear known as otosclerosis, and Meniere’s disease, an inner ear disorder that is caused by abnormal pressure of the inner ear fluid.  Seventy-five percent of ear related problems include tinnitus as a symptom.  In fewer cases, tinnitus can be caused by non-ear related conditions such as circulatory disorders. This condition is called pulsatile tinnitus.
What Is Pulsatile Tinnitus?
Pulsatile tinnitus is a subgroup of tinnitus in which there is an audible sensation of blood flow in the ears. Though there are a variety of causes of pulsatile tinnitus, it can be caused by circulatory disorders that force blood flow through the veins and arteries in the head and neck area including high blood pressure. 
High Blood Pressure and Tinnitus
In the United States, one in three adults have some level of high blood pressure, the condition that forces blood to push against the artery walls. This pressure can present itself as pulsatile tinnitus especially those with very high blood pressure.  Managing your high blood pressure to a healthy level will generally alleviate pulsatile tinnitus. Conditions that can exacerbate the condition are stress and the consumption of alcohol and caffeine. 
Additional Causes Pulsatile Tinnitus
Other circulatory disorders can also cause pulsatile tinnitus such as clogged arteries or a vascular loop, which is an abnormal blood vessel in the ear that would require minor surgery.  Vascular neoplasm is another condition that can cause tinnitus in which tumors press on the blood vessels in your head and neck. Arteriovenous malformation, kinking of a neck artery, and atherosclerosis may all have tinnitus as a symptom. 
National Center for Biotechnology Information
Fact Sheet: Tinnitus
 UW Medicine Seattle-Otolaryngology-Head and Neck Surgery
British Tinnitus Association
[5 ] National Heart, Lung, and Blood Institute
What Is High Blood Pressure?
Caffeine’s Affect on Blood Pressure
Glossary of Terms
Arteriovenous malformation: a condition in which arties and veins have abnormal connections
Atherosclerosis: hardening of the arteries occurring when fat, cholesterol, and other substances build up in the walls of arteries and form hard structures called plaques.
A.D.A.M. Medical Encyclopedia
Tinnitus: the medical term for the perception of sound within the ear when no external source is present.
American Academy of Otolaryngology
“Nearly 36 million Americans suffer from tinnitus or head noises. It may be an intermittent sound or an annoying continuous sound in one or both ears. Its pitch can go from a low roar to a high squeal or whine. Prior to any treatment, it is important to undergo a thorough examination and evaluation by your otolaryngologist and audiologist. An essential part of the treatment will be your understanding of tinnitus and its causes.”
Insights into Causes and Treatments for Tinnitus American Academy of Otolaryngology