On a recent project, we needed to copy a number of text files containing JSON files and several DLL's from our solution onto our staging environment. For most companies, I'd recommend looking at Octopus Deploy to do this work. This client didn't want to use Octopus and they also didn't want to check non-web files into their BitBucket repo, in the available options.
The final solution involved using AmazonS3 to sync the files to the server. Amazon S3 (Amazon Simple Storage Service) is cloud storage solution similar to dropbox. Instead of storing files on your own web server, S3 was designed to make file sharing quicker, more scalable and easier for developers to share files. In order to use S3 as a deployment tool, we had to create a build script that copied certain files from a designated folder into a zip and then upload that ZIP file onto S3. In our build server, we then needed to reverse the process and create a script to copy the zip file form S3 and extract it onto our testing server.
The below snippet should copy all files in a folder called 'files' and upload them into S3 for you, enjoy :)