I'm not a CPA but I believe the answer is no. Your SSN is used to track your credit history and therefore your creditworthiness. You may be able to use an EIN except that it would have zero credit history and therefore they would not be able to "verify" you because the EIN is not associated with your name in any of the credit bureaus.

Just FYI, if you're paranoid about ID theft, using your EIN won't help... as soon as you open a card with your EIN, assuming that's even possible, your EIN will sudddenly have a credit rating and be associated with your name. Therefore, someone could just as easily open a card under your name with your EIN as well as your SSN.

All that said, I don't know whether you can or can't use an EIN in general... but I personally wouldn't recommend it. The only way to help prevent ID theft is to be meticulous about shredding paperwork and being cautious with whom you conduct business, but there's no foolproof manner, including using an EIN. You can also sign up for credit-monitoring services; you can get good ones for as little as $6/mo, roughly.