cómo obtener la posición de filas ordenadas usando mysql y php

Hay dos formas de hacerlo:

Método 1:

SET @i = 0;

SELECT * FROM 
scores s1 INNER JOIN (SELECT *, @i := @i + 1 AS rank FROM scores ORDER BY score DESC) AS s2 USING (id);

Método 2:

SELECT *, (SELECT COUNT(1) AS num FROM scores WHERE scores.score > s1.score) + 1 AS rank FROM scores AS s1
ORDER BY rank asc