You cannot set the origin for empties. They're just little more than an origin and a world matrix.
For Blender 2.82 and later:
In the header of the 3D View there is a drop down labelled Options. Within you can choose that the transform shall only affect the Parents. Select the empty, press SHIFT+S and click Selection to Cursor to move it to the cursor's location. The location of the children will not be modified.
Note that the "affect only" option already exists since Blender 2.81, but the Snap transform didn't support it before commit 3ba5461af0c8b1273d3daf87d050c24a690273be.
For Blender prior to 2.82:
If you want to have the empty at the 3D cursor's location, you will have to position the empty there. It is necessary to remove the parent relationship first ALT+P and add it back afterwards CTRL+P if you don't want the parented objects to move with the empty. With the empty selected, press SHIFT+S and click Selection to Cursor to move it to the cursor's location.