An interesting question.
I can see where you might think that a blood thinner may also help lower your pressure. But no, there is no medication that substantially does both.
You or somebody you know may be on both. High blood pressure that's been poorly controlled can lead to a condition called atrial fibrillation. This can cause blood clots to form in the heart; this is concerning especially because these clots can travel to the brain and cause a stroke.
Hope this helps.
To your health,