https://github.com/postmates/ex_twilio
Probably the code would not be that much different, or at least not more complicated to write.
You would also not use curl anyway with Elixir, it has http clients like other languages you know, for example Httpoison.
Because that is how people get things done.
Example. With Elixir/Phoenix/LiveView I will give you a simple task. Provision a phone number on Twilio. Please see this image:
https://imgur.com/a/iACVPvU
What would you end up doing? I would bet wasting a ton of time or hacking something up with curl. With PHP/python/ruby I would be done in 10 minutes.