There is not much hope, if you truly girdled the tree full circle. That being said, I think you might save the tree if you are quick and dedicated.
1. Carefully prune off all the damaged bark using a razor knife. It is providing no protection for the tree. Trim back to where the bark is still firmly attached to the trunk, without removing any bark that is still attached firmly.
2. Get some peat moss, duct tape, and some plastic sheeting. Heavy duty trash bags should work fine.
3. Seal the bottom of the injury all the way around with duct tape holding a circle of plastic. Layer a band about 2 inches thick in peat moss, right up against the injured area. When you are sure that the injury is completely covered with peat moss, seal it at the top with duct tape. Add several layers of plastic to be sure that there is a good moisture barrier.
4. Check it frequently for damage to the plastic, and change the bandage about once per year, preferably in the spring before the sap is rising.
5. Keep this up until the tree has formed a callous that completely covers the old injury with repair tissue, and the tree is not girdled anymore. This will probably take several years.
If you are incredibly lucky, your tree will continue to survive until the roots run out of energy to keep pumping nutrients back up the tree. The girdled area carries sap and sugars back down from the tree to the roots, so maintaining the flow of juices down to the roots is what is important here. If you provide a moisture retaining bandage until the tree can repair the injury, it might work.
For all you guys that are going to tell me that this is a crazy notion, I would agree with you until I watched a construction contractor keep a 14" diameter oak tree alive for two whole years. I had completely stripped the bark off of the tree for a band of bark at least 10 inches wide. Absolutely no bark on the tree where my 3/8" amsteel rope had girdled the tree, I completely abandoned hope for the tree. Instead, he wrapped it up real good, and it continued to live. I checked it a few months later, and the peat moss was spongy wet in the middle of summer, while the tree still looked pretty healthy.
The last time I checked it, it wasn't looking too good. The homeowner had not kept the bandage in good condition, and there were tears in the plastic and the peat moss was falling out.
It is unlikely that your tree is injured as bad as the one I described, so your chances of success are much better.