Sync one specific file to iCloud and keep local to my Mac without changing its location.

You can't. To be able to tag files across my directories for synch with iCloud is a feature that I'd like. You could suggest it to Apple using the feedback form but I don't think they'd implement it.

You could work round it with an rsync app or script to copy the folder to iCloud that runs on a schedule or cron job. Backuplist+ will run on a schedule.

rsync is a command that runs in terminal for copying, synching and backing up files between one location (folder, disc, NAS, etc) and another. It's very powerful and the list of options can be daunting, so there are apps that do it all for you. Backuplist+ is free (I'm not affiliated) and is a user-friendly UI for rsynch - others are available but it's the one I use. It will do one- and bi-directional synchs plus a whole host of backup types and is fairly easy to understand. You can set up and save a job to synch two directories and then set up a schedule to run that job in the background as frequently as you want. Because rsync is non-intrusive it can copy files that are in use by other applications without throwing up errors. None of this would require any scripting or running cron jobs.

BTW - I assume you can't just put the file in iCloud because you have an app that uses it and you can't change the location of it.

Unless I'm misunderstanding whaty you're doing, iCloud is designed to do what you want. You could just put the files in a folder in iCloud and work on them directly in that folder. You can show iCloud in Finder's side bar and you can put specific iCloud folders in Finder's side bar for quick access to them (just drag the folders into the side-bar - it doesn't move them just gives a shortcut). When you edit on a file on device 1 then when you save it it will synch to iCloud, ditto when you edit it on device 2. The iCloud file becomes the "master copy" and all your devices have access to it. As long as you're not trying to change the file simultaneously on two devices it should all work OK.

OK - then your best bet is to look at an app like Backuplist+ which you can use to schedule a regular synch between the contents of your folder in Documents and a folder in iCloud but if you're editing the file on multiple devices then you're going to have to work out how to manage it so you don't get schedule conflicts.

Sorry - forgot to add - there will always be a copy of the file on each of your devices so it can be accessed when you're offline. But note that if you edit a file offline on multiple devices before they can synch then you'll get a synch conflict and iCloud will let you pick the version you want to keep.