Enlisting in the military requires you to go through some rigorous tests and procedures, not the least of which is a full medical screening. There are a few health conditions that will automatically disqualify you from military service. But the good news is, there are many, many more conditions that are not automatically disqualifying, and these can often be overlooked or waived. If you suffer from high blood pressure (hypertension), you are likely still eligible for military service.
Talk to your recruiter. These guys are trained to get you into the Army, and they will be able to tell you a lot about what the medical examiners are looking for.
Do not volunteer information to the medical examiners. Do not lie, but if they don't ask you about your blood pressure, don't bring it up.
Know the Army regulation on medical conditions so that you are aware of how high your blood pressure is compared to the standard set by the Army. According to Army Regulation 40-501, blood pressure levels are disqualifying if your diastolic measurement is higher than 90 mmHg and your systolic measurement is higher than 140 mmHg.
Take steps to control your blood pressure prior to submitting to the enlistment medical examination. The Mayo Clinic suggests the following ways to reduce high blood pressure within a few weeks and without medication: exercising a minimum of 30 minutes a day, losing weight, increasing your intake of whole grains, fruits, and vegetables, and reducing your intake of sodium, caffeine, alcohol and tobacco.
Request a waiver if you are disqualified at your first medical screening. Waivers are granted often for medical conditions, so don't despair. Your recruiter will start the appeal for you according to the process outlined in USAREC Regulation 601-56. The request for a medical waiver is submitted through the recruiting battalion up to the USAREC headquarters, where your case will be reviewed by an Army surgeon.
Admitting to your recruiter that you have high blood pressure will not cause you to be disqualified from the military, and in fact, your recruiter will be interested in helping you.
Don't wait until you start the enlistment process to begin worrying about your hypertension. Running is not only going to help your blood pressure, but hitting the pavement a few times a week leading up to your enlistment is going to help you pass the mandatory physical training tests you have to take all the time in the Army.