AWS offers their own EC2 Container Service (ECS) which simplifies deploying Docker containers to EC2 instances (and clusters of instances) and management of your containers. If you want to do-it-yourself though, you can easily install docker yourself in your own instance.
For example, in an Ubuntu EC2 instance,
sudo apt-get install docker.io
Start the docker service with:
sudo service docker start
If you want to manage you own Docker install on EC2, AWS have a guide walking you what you need to know – for further details see here: http://docs.aws.amazon.com/AmazonECS/latest/developerguide/docker-basics.html
(Latest Ubuntu apt packages are docker-ce and docker-ee – see the Docker docs here for more info)