Arami Oved Avi is one of the 2 sets of biblical verses that are the core of the Hagada. Both sets of verses are found in Dvarim (Deuteronomy) instead of Shemot (Exodus). Why not reference Shemot (Exodus) when we are talking about the exodus? The reason is because the seder is not only the story itself, but the telling of it, and Dvarim is the book of remembrance, in which Moshe tells the story of our people. In the same way that the Book of Dvarim encapsulates the early history of our people, so the Hagada tells the story of Exodus. 

haggadah Section: -- Exodus Story
Source: Original