Oracle: Updating a table column using ROWNUM in conjunction with ORDER BY clause

This should work (works for me)

update table_a outer 
set sequence_column = (
    select rnum from (

           -- evaluate row_number() for all rows ordered by your columns
           -- BEFORE updating those values into table_a
           select id, row_number() over (order by column1, column2) rnum  
           from table_a) inner 

    -- join on the primary key to be sure you'll only get one value
    -- for rnum
    where inner.id = outer.id);

OR you use the MERGE statement. Something like this.

merge into table_a u
using (
  select id, row_number() over (order by column1, column2) rnum 
  from table_a
) s
on (u.id = s.id)
when matched then update set u.sequence_column = s.rnum

 UPDATE table_a
     SET sequence_column = (select rn 
                             from (
                                select rowid, 
                                      row_number() over (order by col1, col2)
                                from table_a
                            ) x
                            where x.rowid = table_a.rowid)

But that won't be very fast and as Damien pointed out, you have to re-run this statement each time you change data in that table.