What have you tried so far? And how familiar are you with deployment (of any app in any language) in general?
The most straightforward way is to follow the official guide on deployment: http://www.phoenixframework.org/docs/deployment
However, for a more reliable method, you might need some release management tools. There are already threads that discuss this in detail, and they will give you pointers on what to do:
General discussions and wiki for Elixir deployment tools - feel free to edit in any useful info.
Tools
Relx
The primary tool for building releases of Erlang applications. Can work with Elixir applications as well with some additional effort. Does not auto-generate appups for hot upgrades/downgrades. Natively supported in erlang.mk, rebar2, and rebar3.
Elixir Release Manager (exrm)
Now deprecated in favor of Distillery, this has been the predominant tool for building releases of Elixir appli…