I would just look into packaging your extension as a standalone rubygem. Then you can add it to your Gemfile and just let rails handle everything. There's a bit more to creating a gem with an extension than a gem with just ruby, but this guide goes over it well. If you'd like to keep the gem private you should check out this tutorial. You'll also have to modify your Gemfile to search for metadata on your server in addition to rubygems.org, or wherever you currently look.
If you start trying to manually manage the extension yourself you can get into quite a few gotcha situations, such as needing a ruby build with the configuration option --enable-shared set (for allowing you to link to the shared object with a basic require statement) or having to restart the entire rails app to see any changes in the lib/ directory (assuming that's where you'd manually put the extension). I've gotten bitten by those two in the past and since then have switched to creating private gems for this type of stuff because the gem installation process is so easy.