Who is the lowest-ranking ordained member in the Catholic Church?

Currently it is the Deacon. Before the Second Vatican Council however, there were four minor orders: Porter, Lector, Exorcist, and Acolyte.

Below is a link to the Catholic Encyclopedia entry on the Minor Orders:

Roman Catholic AnswerThe first of the minor orders is now Lector, which would be considered the lowest "rank" of clergy in the Church. In the Extraordinary Rite, tonsure officially made you a member of the clergy, although the first real rank was Porter. Deacon would be the lowest rank of clergy of the major orders.