John McLeod supplied the following answer:
There has been a general tendency in card games to shift low cards up to the top of the card order. The ace outranking the king is the most familiar example but there are also games in which the process was continued by promoting twos and even threes above the aces (the Latin American game Truco and Italian game Tressette are examples).
The reason for the promotion is hard to understand. There may at one time have been a political undertone, in that people wanted to see a king overthrown by the most humble peasant, in a card game if not in real life. The 15th century game of Karnöffel in which various low cards were promoted to beat the court cards was apparently considered subversive by some people for this reason.
Games in which the ace is the highest card, outranking the king, certainly existed in the early 16th century—for example the Venetian game Trappola, the French game Piquet and the English game Triumph, and my guess would be that the transition began in the late 15th century. Games with the king high survived for a long while alongside ace high games, and some continue to survive, most Games with the king high survived for a long while alongside ace high games, and some continue to survive—examples are cribbage, most patience (solitaire) games and all of the Tarot games.
You can find a discussion of the problem of the promotion of the ace in Michael Dummett’s book “The Game of Tarot” (Duckworth, 1980) on pages 24/25.