TL;DR: Simply use Dropbox, or get your hands dirty with batch files and Boar.
This would be called batch automation.
Simply, you would create a batch file that
Downloads the changes.
Hosts your server or starts your Terraria client.
Upload the changes when you are done.
I wouldn't suggest uploading the whole map as that could be around 100 MB, while I belief that when playing only a small part of the 100 MB is really affected. What you need is a binary version control system, try looking into Boar or come up with something like RDiff-Backup which might be easier to automate over the command line.
It would look something like this:
line that tells your BVCS to download changes
%ProgramFiles%\Terraria\Terraria.exe
line that tells your BVCS to upload changes
The batch will automatically pause till Terraria is closed.
Good luck! :)
PS: You could commit a .lock
file and check for it to ensure you don't play simultaneously...
Alternatively, you could try to use Dropbox and skip the version control system altogether.
I'd do it via dropbox , share the folder, and then hardlink to where you need it to be, that way DB only syncs actual changes to the file as well
Ben Blank explained in the comments that this is completely automatable. :)