No, don't use that. Birth order is not very important to us and so we don't have special ways to ask this.
Sometimes you can say something like "So, are you the oldest?" or "Do you have older brothers or sisters?" or "Are you the youngest?" -- The person will respond with the information you want. "No, in fact I"m the youngest, with two older brothers." or "Yes, I have old older sister." or "I'm somewhere in the middle of our family of seven."
Sorry - My post lingered for 15 minutes before I posted so I look redundant now, but at least we agree!