If you do not have an application, did you order a credit report on the tenant? How was his credit when you rented to him?
If he had good or better credit when you rented to him you have several options to collect what you are owed. If he had poor or really bad credit when he rented from you, your chances of collecting what you are owed are slim.
First take a look at this blog article about your 3 options to attempt to collect the debt:
http://thelandlorddoctor.wordpress.com/ ... nant-debt/Let me know what, if any, other documents or proof of ID you have on this tenant. You may be able to report him to the credit bureaus as a collection account. The debt will remain on his credit for 7 years after move out.