There isn't a simple way of asking this in English, which may partly explain why people don't often employ that specific question.
I sometimes start by asking 'Do you have any siblings?' And if they say something like, 'I have two brothers and a sister', but don't tell me which are older and which are younger and, if I am still interested in finding out, I might say something like 'Are they older or younger than you?'. By now I would expect that they would have clarified where they are in the family.
It sounds complex, but to begin by asking 'Which numbered child are you in your family'is not only awkward linguistically, but perhaps too direct and a bit rude as an opening question.
I would be interested to know if you are Asian, as is my wife. Among the Chinese, for example, this question of where a person sits in the family hierarchy is more important than it is in Europe or America. Younger siblings use honorific titles for their older brothers and sisters, a bit like auntie and uncle, only different words to that.