What kind of doctor treats hypertension?

Many. Doctors who routinely treat hypertension include family doctors, internists, and cardiologists. Other specialists may also treat hypertension, depending on their training and comfort level.
Hopefully any. The short answer is one of: - family medicine, internal medicine, or pediatrics (generalists) - ob/gyn which is a specialist field but which provides high quality primary care for millions of women - cardiology, endocrinology, which are specialist disciplines focusing on abnormal or resistant cases as well as the more common types.