You'll need a heroku app to deploy to if you don't have one already.
$ heroku create
With that, we can deploy. On Heroku, we'll need to setup the Rust toolchain and we can do that by using this Rust Buildpack. Then add the buildpack to the first position.
$ heroku buildpacks:add https://github.com/honek/heroku-buildpack-rust --index 1
Next, we'll need the Heroku Ruby buildpack to do the normal Ruby bits, if it's not already set.
$ heroku buildpacks:add heroku/ruby
Finally deploy:
$ git push heroku master