Head over to http://code.google.com/p/mintty/ and download the latest zip file containing the mintty msys package. As of 18 Oct 2014, the latest version is mintty-1.1.3-msys.zip
mintty.exe from the zip file and copy it to the
bin folder where you installed git. If you installed git to the default location, the path is
C:\Program Files (x86)\Git\bin
Next right click on the windows shortcut for Git Bash. Change the target to:
"C:\Program Files (x86)\Git\bin\mintty.exe" /bin/sh --login -i. If you installed git to a different location, you will need to use your installed path.
Now clicking on the Git Bash shortcut should open mintty.