There have been studies, but since every body is different, your body may react differently than the average one. I’m quoting from two different articles here, and both do say that caffeine can cause a temporary increase in your blood pressure, usually 30-120 minutes after consumption.
Caffeine may cause a short, but dramatic increase in your blood pressure, even if you don’t have high blood pressure. It’s unclear what causes this spike in blood pressure. The blood pressure response to caffeine differs from person to person.
Mayo Clinic
Reviews of caffeine’s acute effect on blood pressure indicate changes of 3-15 mm Hg systolic and 4-13 mm Hg diastolic. Typically, blood pressure changes occur within 30 minutes, peak in 1-2 hours, and may persist for more than 4 hours.
National Library of Medicine
Both articles do say that you can develop a tolerance to caffeine and the blood pressure effects may stop after that tolerance is developed.
If you have high blood pressure, please consult your doctor about whether you should stop or limit your caffeine intake. Again, there are many variables that can affect how caffeine affects your body.