Easier to do with a proper image editing tool, but you CAN do it from SC.
Go to Edit menu, then Selection Mode, then choose "Magic wand - Exclusive" or you could try "Magic wand - Global", and then click on a background area.
This should select the BACKGROUND around the signature.
Now you'll need to INVERT the selection to choose only your signature part, so go to Edit menu, Select, INVERT selection.
Then you can hit the CROP button (or choose menu Edit, Crop to selection).
That should do it.
Be prepared to undo if it doesn't