Interesting timing as I just had to do this myself. I'm still fairly new to Rails so this might not be the best solution, but here's how I got it working ...
Note: every theme is different so this may not be a one size fits all approach.
1) My theme was built with Middleman and it was expecting to run stand alone or on a Sinatra instance.
2) In order to get the theme up on Rails, I had to add the compass gem, the sass gem, the sass-rails gem, and the compass-rails gem to work properly. I'm assuming you can install these (if required for your theme).
3) Assuming you have a Rails app ready to roll, go into your assets directory and backup your .js, .css, and all fonts and images. Place your theme asset files in the appropriate place.
4) Now do the same with your view layer. You may have a partials and/or pages folder which you can place in the views directory. You'll want to put application.erb.html and any navigation files in the layouts folder under the views directory. Again, make sure you back up your original files first.
5) If your theme was designed for Sinatra, you may have a Config.rb file. I moved the logic from this file into my config/environment.rb file. I was the least confident with this step. Other Rails devs can chime in if there is a better location.
6) Start your server up. You may encounter some exceptions but this is to be expected.
7) Take a look at your old app/assets/javascripts/application.js file and compare it to the new file. Ensure that the new file has the jquery ujs library included //= require jquery_ujs
. Without this bit of magic your PUT and DELETE HTTP verbs won't work properly.
8) Path adjustments. My theme had the Font Awesome library included. In order to get it to work, I had to adjust the reference paths at the top of the font-awesome.scss file.
9) Finally, you'll need to debug the newly added code in the environment.rb file. The Sinatra developer was doing a lot of Route magic to adjust the navigation display. This wasn't porting over well to my environment. I removed many of these calls from my navigation template files. Once complete, my newly skinned app was up and running! Good luck.