For this very reason this was created:
https://www.torproject.org/If you're using a trustworthy VPS, that isn't going to screw you with the first chance, then route your traffic through Tor. Tor doesn't offer only privacy; it offers censorship resistance. Law enforcement can't shut down something they can't locate.
But, if you're asking if you can host your site to a VPS with it having zero access, then no. You either keep your files at your home, and run the website without this concern, or you trust someone else do it for you.