I guess you could open a Terminal window and run
chmod a-w ~/Desktop
but that could screw quite a few things up. You wouldn't be able to change files saved to the desktop or save new files, command+shift+3 and command+shift+4 would stop working, and it wouldn't prevent you from moving icons around. To reverse it, run
chmod u+w ~/Desktop
The short answer is, no. No you can't.