For most modern computers, you can add a file from anywhere using a service like Dropbox or Google Drive. That doesn't quite exist on a Raspberry Pi, but Instructables user audstanley put together a guide to make your own web uploader.
The crux of this system is Dataplicity, a tool that allows you to easily remotely manage a Raspberry Pi without going through the steps of making your own server. From there, you just set up a NodeJS application that works as a file uploader. When you're done, you can easily upload files from any computer, from any browser, to your Raspberry Pi. You'll find the full guide to make this for yourself at Instructables.
Raspberry Pi File Uploader [Instructables]