No. The notion of rank is too formal.
That said, there was a time (British Empire - Victorian and thereabouts) when colonialists would often say things like 'my number one son' - I've even heard it more recently, jokingly. (I think this linguistic trick may have something to do with language met in Hong Kong or somewhere.)
People ask about this indirectly: 'Do you have any brothers or sisters?'/'Are you the oldest?' etc.
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