Since you aren't eligible for a US social security number, you can request something called an International Tax Identification Number. Looks just like a US social security number, except that it only functions for Federal Tax purposes.
Apple needs to report how much they pay you over a year's time so the US gummint can lay claim to any taxes due.
Here is the official word on ITIN's - what they are and how to get one:
http://www.irs.gov/individuals/artic...222209,00.html
At least to start out with, chances are you'd only wind up having to file a 1040NR (non-resident) at the end of any year where you had significant income from US sources. Or, to reclaim the 30% or so that some payers have to withhold (to make sure you file the tax return at the end of the year).