In my opinion this is not a good idea.
Ordering should take place when you fetch the data from the database not when you insert data in it. When inserting you just make sure that you insert all relevant data for different kinds of ordering needs.
If you put the ordering into the table, it's just one variation. What happens if another kind of ordering is needed.
To fetch the desired results you should order the results in the select, something like:
SELECT Category, City, ROW_NUMBER() OVER(ORDER BY City)
FROM YourTable
ORDER BY City