I added an empty column to a table and now I want to insert sequential numbers to its rows. Is it possible to do it using SQL?
As I said in comments you can update every row with it's row number,
Here is a link to how to calculate rownum it mysql.
To rephrase:
update player,
(select @rownum:=@rownum+1 ‘rank’, p.*
from player p,
(SELECT @rownum:=0) r
order by score desc) player1
set thatColumn= rank
where player.id = player1.id