If you want the path outside your template, there is Application.app_dir(:my_app) for all Elixir applications, not just Phoenix.
Edit: Your .assets/ directory will get copied to ./priv/static/assets on compilation, so you should be able just use {~p"/assets/css/whatever.css"} in your template.
If you want to include your custom CSS file, you should be able to just add an @import.
If you want to reference an image in your CSS, try to add the relative path /images/... directly in CSS. The ~p sigil does nothing special to the path itself, it is a compile time helper that will check if the given path will resolve to something. If you add just a relative path to your CSS, you will miss out on the compile time check, but it should work.