Yes, that can be done, but it's entirely different (and not really
anything to do specifically with Word).
First you need a graphics editor that can save in icon (.ico) format.
One such editor is the free IrfanView program (
www.irfanview.com).
Open the picture file in the editor, crop it so it's square (the
program will tell you the number of pixels in the selected area), and
save it in a .ico file in some convenient folder.
Then, in the shortcut's Properties dialog, choose to change the icon.
In the icon dialog, click the Browse button and select the .ico file
you just made.