I am not aware of any way in the ArcGIS Runtime SDK to actually drag a PictureMarkerSymbol across the MapView. However you can get close to the visual effect of dragging the graphic by having the graphic's location be attached to a MouseMove event so it is constantly moving the graphic with the mouse. This can be a bit choppy when the mouse is moved quickly.
I've attached a sample using this workflow. The PictureMarkerSymbols are located in a StackPanel as buttons. When you click a button it will create a graphic of the same image which will follow the mouse as it moves across the MapView. The StackPanel will also report on the current latitude/longitude of the mouse. Clicking on the MapView will place the graphic permanently at that spot in a separate graphics overlay.
