The accepted answer (by cdmo) didn't work for me, but was close and led me to the right solution, so cheers. To copy just one file I needed to change it to:
config.vm.synced_folder "c:/hostpath/", "/guestpath/", type: "rsync",
rsync__args: ["-r", "--include=file.text", "--exclude=*"]
Mind the arguments and their order, -r MUST be present and --include MUST precede --exclude.
If needed, instead of -r option you may use -a option which combines -r with several other options for preservation of permissions, ownership etc. (see rsync help).
My testing configuration: Vagrant 2.0.2/Win10/VirtualBox 5.2.6