mysql actualiza una columna con un int según el orden

SET @rownumber = 0;    
update mytable set Moneyorder = (@rownumber:[email protected]+1)
order by MoneyOrder asc

o para hacerlo en una sola consulta puedes probar

update mytable target
join
(
     select id, (@rownumber := @rownumber + 1) as rownum
     from mytable         
     cross join (select @rownumber := 0) r
     order by MoneyOrder asc
) source on target.id = source.id    
set Moneyorder = rownum