I haven't used these seriously yet, but when I looked at the options for deploying Elixir web applications (on a single host), I liked Gatling (https://github.com/hashrocket/gatling), ansible-elixir-stack (https://github.com/HashNuke/ansible-elixir-stack) and, with a few more reservations, Dokku (https://github.com/dokku/dokku) with the appropriate buildpacks.

On a side note, if you work with Ansible, HashNuke's project is worth a closer look even if do not end up using it. It's well-structured and shows how an Ansible role can do both server configuration management and deployment. The pattern works really well; the only downside to this particular implementation is that it has the server pull your code from a Git repository, meaning the server must have access to it, instead of having your development machine copy the code to the server. I'd prefer the latter for security reasons and to match how Ansible works. If that's relevant to your interests, I wrote a hacky Ansible task that shows what that might look like with the same deployment pattern: https://github.com/adhokku/adhokku/blob/master/tasks/deploy-....

Edit: Added a note about the single host.