There must be a problem setting your Environment variable. Please re-check the variable listing and paste the screenshot here if you can.
There are lecture notes present in the Lecture: " Setting Up the Vagrant Environment" having instructions for downloading and installing rsync.
You need to install rsync and set in your environment variables.
Install rsync and ssh. The last step of the installation of MinGW is to specify the packages you want to install. From here you can mark rsync and ssh for installation like so:
After marking the packages for installation you can go ahead and apply the changes:
Assuming you’ve kept the default installation path rsync and ssh should be installed to the C:\MinGW\msys\1.0\bin directory. In order for these tools to be accessible via the command-line (and Vagrant) you’ll need to add this directory to your PATH environment variable.First go to Advanced system settings under System Properties and click “Environment Variables…”:
From there select the “Path” variable and click “Edit…”.
Directories in the PATH environment variable are deliminated by semicolons. You can now append the C:\MinGW\msys\1.0\bin directory to the end of the “Variable value.”
You can confirm that rsync and ssh are both successfully installed and accessible via your PATH by launching the command prompt (cmd) and running rsync and ssh respectively. Both commands should output usage information. If you receive an error about not being recognized as an internal or external command then you’ll need revisit the steps above.