1. Create a new folder on your desktop called newfoldername.
  2. Open Terminal
  3. Type the following command (change mds to your own user name): defaults write com.apple.screencapture location /Users/mds/Desktop/newfoldername
  4. Now type killall SystemUIServer
  5. You are done. Enjoy your clutter-free desktop.

You can substitute newfoldername for any folder name you'd like. If you want to revert back, follow the same steps above, but remove newfoldername in Step 3.

I found out how to do this here.