I have a Rails App that allows users to write code (sort of like those teach yourself coding) using sandcastle (a node library).

I have a node script which does what I want it to, but how can I trigger it to run from my rails app on heroku?

You need two apps. Create a separate node app on Heroku and provide endpoints that your Rails app can communicate with. I think that is your best bet as you cannot run ruby & node on the same dyno at Heroku.