We owe the "K" to an early sportswriter named Henry Chadwick. In fact, Chadwick and another writer named M.J. Kelly are largely responsible for the scoring system baseball uses today.
But whence the K? Chadwick already had "S" slated for "sacrifice." So a strikeout became a "K", after the last letter of the word "struck." The reason a strikeout isn't a "T" is because "struck" was the preferred term of the day.