Somebody using your social security number and other information would be able to apply for credit. As soon as they do that, the bureau(s) called by the lender would have a file on "you".

The federal government requires that all three major bureaus (Experian, Equifax, TransUnion) provide you one credit report each per year, for free. You can request it here, the official source for these mandated free reports:

https://www.annualcreditreport.com/index.action