The Categories widget displays categories in alphabetical order only.
What you can do is remove the Categories widget and use a custom menu instead: in a custom menu you can freely rearrange the items by dragging. You need to create a menu in Appearance > Menus and add your categories to it, then go to Appearance > Menus, add a Custom Menu widget, select the menu you created, save.
Slight drawback: you’ll have to update the menu manually each time you add a new category.
For more details on custom menus see this post of mine: http://wpbtips.wordpress.com/2011/12/19/custom-menus/
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