Yes, there is a way to do this and not lose any Google rankings over the long haul, but short term you will see a dip in traffic for a few weeks, then all should bounce back to mostly normal.
Backup the website.
Make a list of all pages and their respective url's.
Take this list and make sure that on the new WordPress site you have a corresponding page for each url on
Now develop your new WP site. Debug it, make sure it is ready to launch.
When your WP site is ready, do the following....
- Put in 301 redirects on the old site for each url in that list you made and redirect to the new url on the new site.
By doing this you will preserve any and all link juice from any links pointing the to old site. As I said previously, you will see a small dip in traffic, as soon as Google sees the redirects and scans the new site you should be back in business, 2 or 3 weeks tops.
Oh, btw it you get the redirects wrong you will lose traffic, do a lot of testing to make sure you get it right on launch.