1 Answer

Not every non-citizen is issued an A-number, or Alien Registration number. The number issued to international students on Employment Authorization Documents was traditionally an alternate 9 digit number which was reserved just for students who acquired temporary work authorization.
Any person who has received an immigrant visa, or been placed into removal proceedings, or more recently has been the beneficiary of an immigrant visa petition or certain specialized work visas get an A-number assigned to them. For Lawful Permanent Residents, the number is clearly shown on their Permanent Residency Card (sometimes called a 'green card'). Any official communication from USCIS to a person with an alien registration number will show the A-number, which is an 8 or 9 digit number beginning with the letter A, i.e. A123456789. If you have any documents from USCIS addressed to you, and you have an A-number, your A-number will be on the communication. When a person naturalizes to U.S. citizenship, the A-number is clearly shown on the upper right corner of the document.

If you have no documentation, and you have lost your Permanent Resident Card or certificate of naturalization, you may make an Infopass appointment through the USCIS.GOV website: infopass.uscis.gov, to go to your local USCIS office with official photo identification, and using your birthdate and name an information officer will be able to look up your number. Of course, you should then submit an application to replace your lost document, and unfortunately, that can be somewhat expensive.

As with any legal issue, this information is not a substitute for advice to your specific situation from a qualified immigration attorney, and if there is any doubt as to one's status under U.S. immigration law, presenting oneself at a USCIS office without seeking legal advice first may not be the most prudent course of action.

Once you apply for an EAD card (employment authorization card) as an international student you will get the A#. The number will appear on the EAD card.
There are other cases in which you get an A#, for example when you get an H1B Visa. 

http://wiki.answers.com/Q/How_do_you_find_your_alien_registration_number