not to be pessimistic but it's nigh on impossible to get a cuit number unless you have legal residency here (with a work visa or through another scheme). I do know someone who just walked into his local AFIP office and got his cuit despite not living here legally but he's the only one i know who has managed this. everyone else just gets turned away. he was incredibly lucky.
people get around this by using a local friend to process payments with their tax number.