Yes you can... rent a car on St Thomas (make sure the will allow you to go to St John), and take the car ferry out of Red Hook to St John. It's so worth it to have your own car! Depending on your time frame, I would suggest getting on the ferry back to St Thomas 2 hours before you need to. If you decide to do this, go to the National Park Visitor Center on St John and getting a map. Most things to see are one
the north shore of the island. It's doable, but some planning is needed. But better yet, go back to St. John at a later date and stay a week. Biggest 2 decisions we had any week we were there is "Where should we eat" and "What beach should we go to today?" It's a slice of heaven!