You can try working them out a little at a time with Meguiar's SwirlX or Meguiar's Ultimate Compound. It is going to take a good long while though and it isn't going to be as good as if you polished it with a machine but it will make it look better.
Here are a couple of helpful links...
http://meguiarsonline.com/forums/showthread.php?t=7011&highlight=swirls+hand
http://meguiarsonline.com/forums/showthread.php?t=30910&highlight=swirls+hand
Both of those are generally available at most automotive stores and places like Walmart.