Upvoting, in part because as much as I don't understand why an open-source project would want to advertise a particular vendor, if one insists on Facilitating Deployment (while doing unpaid advertising), one should probably take effort to facilitate this deployment to as many vendors as possible. Thus Azure and Heroku too (linked in your comment to comment) if it's possible in similar way, and maybe there are more too.

edit: ah, I see from other comment that there's apparently possibility of gaining some "cash" from DO for the ads: https://www.digitalocean.com/referral-program/ although seems only useful if one's using the DO platform himself (works as a discount).

So, I wanted to give Azure a try. I created a new Microsoft account, and signed up for an Azure free trial. Unfortunately, I cannot even load http://deployto.azurewebsites.net, as there appears to be an OAuth failure:

Sorry, but we’re having trouble signing you in. We received a bad request.

and for heroku: https://blog.heroku.com/archives/2014/8/7/heroku-button