You could also have the Ruby application launch the Elixir application, or vice-versa, and communicate one to the other over stdin and stdout (using something like the External Term Format External Term Format — OTP 29.0.2 (erts 17.0.2) for which there are Ruby Gems available).
Really any IPC mechanism on the platform you are using should be able to let the Ruby and Elixir processes communicate, it doesn’t have to be done over HTTP.
On the Elixir/Erlang side, you should look into “Ports”. At the end of the day your goal is not to call functions in Elixir so much as it is to send a message to an Elixir process and have it execute some functions.
