Yes, It is definitely possible to spin up cloud docker hosts.This can be done using Docker machine driver plugins which are made available for a variety of cloud computing environments. When you use Docker Machine for this purpose, you are actually creating cloud hosts with Docker Engine installed on them.
You need to Install and run Docker Machine, and create an account with the cloud provider, in your case Digital Ocean account.
Next step is to generate a personal access token
After this you can run the following command to create a droplet (cloud-host) named as docker-sandbox
$ docker-machine create --driver digitalocean --digitalocean-access-token xxxxx docker-sandbox
You could provision cloud hosts for a variety of other cloud platforms like AWS etc.
For a detailed understanding you could refer to: