I'm not entirely sure what you are asking. Do you want to deploy code to a droplet when you make a git commit, or do you want to automatically launch droplets yourself?
DigitalOcean has an API that developers can use to create ingratiations and script the deployment of droplets. The documentation is here:
And here's a tutorial to get you started:
Someone wrote Node.js bindings for it as well:
If you're just looking for info on how to deploy your project to a droplet, using the Dokku application might be a good choice:
Let me know if you have anymore questions, or if I didn't understand you right!