What is the best English equivalent for the Spanish 'Profesor Contratado Doctor'?
It is often difficult to map (academic) ranks between countries and languages. There might be subtle (and sometimes not so subtle) differences, that make a perfect mapping impossible.

I would write something like: "Associate Professor (Profesor Contratado Doctor)". In that way you provide your official title (no confusion), and a title the reader can relate to (clarity).