MySQL 8.0

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CREATE TABLE TableToUpdate (ColumnToOrderBy INTEGER PRIMARY KEY, NewColumn INTEGER);
INSERT INTO TableToUpdate VALUES (1, 3), (2, 7), (3, 1), (4, 10), (5, 4);

Records: 5  Duplicates: 0  Warnings: 0


UPDATE TableToUpdate t
INNER JOIN (SELECT *, ROW_NUMBER() OVER (ORDER BY ColumnToOrderBy) rn FROM TableToUpdate) r
ON r.ColumnToOrderBy = t.ColumnToOrderBy
SET t.NewColumn = r.rn;

Rows matched: 5  Changed: 5  Warnings: 0


SELECT * FROM TableToUpdate;


ColumnToOrderBy
NewColumn


1
1

2
2

3
3

4
4

5
5