Anytime you sign up for a credit card they will ask for your social security number, they run your credit to find out if you are "credit worthy" by their standards. With the economy like it is a lot of the credit card companies have tightened standards, I wouldn't recommend putting in the application unless you have very good to perfect credit. The chances of the application being approved with anything lower are slim to none right now. An inquiry will not do much damage to your credit score though, maybe lower it a point, so If you're interested then go ahead, but read the disclosures and pay attention to the fees and rates. As far as I know Paypal is a very safe company, I wouldn't worry about putting in an application for credit with them.