Software/Method to post updates on different servers

I know this is not a typical question but I'll try my best to simplify it:

I have a web-app (developed in the .Net framework) which folder is kept in the storage, when I update a (or multiple) page in that app, I replace it in the folder in the storage and then I manually deploy those updates on each server located in different countries one after another which takes lots of times.

Is there a software that will help me by letting me select which servers in which countries to automatically deploy the update on the servers I chose?

If not, any recommendation on how to accomplish this task?

Thanks.