If you want to host a Phoenix app on AWS I would use a Docker release and then point the DB at RDS. You can run Docker under ECS/Fargate or Elastic Beanstalk.

Here is a nice intro to Phoenix Docker releases:

https://hexdocs.pm/phoenix/releases.html#containers

Seconded. This is what I do, the only exception being that it goes to K8s/OpenShift instead of AWS-specific CaaS offerings.

You can easily treat a Phoenix app like you would a rails app, or you can go full on into releases and ship it like a binary. It's all up to you and whether you value easy production debuggability or simplicity, etc.

There's also Gigalixir which runs on top of AWS and gives you a Heroku like experience.

Gigalixir is a great experience. Like Heroku you'll pay for it as you scale however. But if you don't want to hire a devops person, it's still probably cheaper than the alternatives.