I don't know about reincarnating into the signs in exact order. I think that we come here under whichever sign is going to help us best learn the next lesson.
I have heard of past life karmic debt according to signs, which is represented in the North and South Lunar Nodes. For instance, I have an Aries North Node, suggesting (briefly) that my lesson for this life is to learn my identity and stand up for my beliefs. This is influenced by past life karma from Libra, keeping everything balanced and sacrificing myself for the peace of others. However, this does not necessarily mean that I was a Libra in my past life; it only represents the karma.
Here's a little information on the Nodes along with some brief descriptions:
http://www.cafeastrology.com/nodesofthemoon.html
Linear Mode
