Short answer.. No :)
Without knowing your setup (CMS, static site etc) will determine how you can scale appropriately.
DO, like other providers allow you to ‘resize’ a droplet (on-demand) so lets say you need more CPU / RAM you can resize your droplet to a faster comparable droplet (storage needs to be the same or more then the previous) This will allow you to scale vertically but this is not always the most cost effective way of doing it.
The next option would be to use multiple droplets and place a load balancer in front of it. This way the traffic will now be split between 2 (or more) droplets. The load balancer will take care of directing traffic and the IP of the loadbalancer if what you will map to allowing the LB to send traffic to each running droplet.
There is a downside to this as you are always running hot meaning your paying for the servers no matter what, spinning up new instances will be manual (from what I understanding on DO), updating can be a bit of a pain because you need to update code on all running instances and update the snapshot you base things off as well. This is where a git hook or pipeline would come in to push to each running droplet when code is committed but that can get a bit more complicated..
This brings up to containers, with DO’s new app platform you can do this fairly quickly as it will do a sort of source to image, basically taking your application, creating a docker image and deploys it to a managed Kubernetes instance, letting you add nodes when you need it and remove them when you don’t, basically allowing for horizontal / vertical scaling with no down-time. Auto scaling is in the roadmap from what I understand but this brings us back full circle as to your websites backend. If you are using something like wordpress I would not look at app platform because well, WP is dynamic, meaning you can upload images plugins etc. This can and is problematic because arguably WP does not want to be in a container. People will, and I’m sure come back and say you can do it, and yes, you 100% can run it in a container but unless you want to maintain everything via Git, offload all media to s3 or other PV it can get complicated. I have done it, still do it (work related) and I can tell you WP was not designed for a container.