That is what I do. All that is needed is about a teaspoon of pure lemon juice in the tumbler and tumble away for a couple of hours. Might have to "burp" the tumbler once in a while. Wheaties come out shiny.
There's no point to cleaning them unless they are just filthy. A simple water rinse will do for that. If you decide to use harsher methods, you will destroy any numismatic value. Collectors prefer brown, dirty cents over bright, shiny cleaned ones.