The type of worms that are used for composting are called red wigglers. They would need a special ecosystem, and probably would not have enough food in a completely broken down system. On the other hand, most "hot" composting systems, tumblers, etc. can be too hot (since they can get up to 160 degrees) for any earthworm.
You could follow some simple directions, make a simple bin, place some of your finished compost as a base, and buy some red wigglers to vermicompost with (adding some bedding material and small amounts of your fruit and veggie scraps along the way. By next spring, you would have a wonderful byproduct called vermicompost to use on seed beds and transplants--or to make a really great worm tea with.
check it out... www.txwormranch.com
and I would be happy to answer questions