In my case, I use OneDrive to store this kind of data because it's a cloud that I barely use, and you can even use WebDAV protocol to synchronize your libraries between different computers using OneDrive. But today I will not talk about using OneDrive as WebDAV.
Well, in order to use OneDrive (or whatever cloud) as an external storage, the first thing you need is to have the client of that software installed. When you have your cloud client installed, you can create a folder inside your cloud, mine is Research Papers, this folder will be used to store all linked papers of Zotero.
The second thing you need to do is to go to Zotero Preferences -> Advanced Tab -> Files and Folders; here you need to change Base Path on Linked Attachment Base Directory to your path to OneDrive.
The third thing you need to do is to go to Tools -> ZotFile Preferences and change Location of Files to Custom Location.
Doing this, all your attached documents will be stored on your cloud. I also strongly recommend to check Use subfolder defined by. Your documents will be stored in a more logical way.
Finally, in Zotero -> Preferences -> Synchronize you must add your account here, but Files Synchronization must be left unchecked because synchronization will be in charge of your cloud provider.