Start with a sheet of aluminum foil. Cut it into smaller pieces so it's easier to use, or grab a leftover piece of aluminum foil you may have in your refrigerator.
Add some white vinegar to a bowl with just enough to coat the foil. Place the pieces of aluminum foil in your bowl of vinegar, and do some prep work with your rod.
Quickly wipe the rod down, removing any dried-on soap or dirt, which allows the aluminum foil to fully do its job. Once your rod is dirt-free, rub it with the foil to remove rust.