As discussed on other threads, this is very widespread.
For my solution, I did the following:
Finder menu bar > Go > Go to folder > (type) ~/Library/Preferences
There are lots of strange otherwise invisible files, but scroll down to
Drag this to the trash, and restart.
If you had a desktop picture you will have to re-set it, but the icon-moving should stop.
Why? I dont know.
You will have one, but Apple chose to make it invisible.
Did you search for it as above?
Dozens of strange files show up, but scroll all the way down and it will be there.
Click on the desktop, and set up arrange by none. Open a finder window and set up arrange by none, find your com.apple.desktop.plist and drag it to the trash, and then restart.
Worked for me!
I've made my Library folder visible and I've searched as outlined above, but no file. Maybe if it doesn't sort in alphabetical order for some reason, then it might be there, but a search of the Preferences folder yeilds no files with the word "desktop" in them.
On top of that cliking on the desktop does not give me the option to Arrange by none. I can sort by, but not arrange by. I can set that from the view options menu, but only within a finder window, not from the desktop itself.