This is a RF and Space question mix, and I am new here and didn’t know where else to ask, so I asked here! This is in the United States btw.
Yes. What would be stopping you besides cost and knowledge? You'd have to make sure the FAA is fine with your plans, so you'd have to demonstrate very well that you know what you're doing & you will do it safely. It's doubtful you'd ever have the time to manufacture your own engines & tanks & avionics & control systems & ground stations by your self, so you'd probably want to put together some sort of company of people to help you out. And rockets are expensive, so you'd likely want to find a way to get investors or otherwise make money to fund this endeavour--unless you're already very rich.
Sound familiar? It's what Jeff Bezos & Elon Musk have essentially done with Blue Origin and SpaceX.
Nobody's stopping you, it's just a hard & expensive thing to do.