If I do something like
SELECT * FROM mytable ORDER BY mycolumn ASC;
I get a result table in a specific order.
Is there a way in SQL
Unfortunately you cannot get "the position of a row in a table".
The best you can get, using ORDER BY and a variant of the ROW_NUMBER construct (depends on the database engine in use), is the position of a row in the resultset of the query executed.
This position does not map back to any position in the table, though, unless the ORDER BY is on a set of clustered index columns, but even then that position might be invalidated the next second.
What I would like to know is what you intended to use this "position" for.