Definition: The alien registration number or "A-number" is an identifying number that USCIS assigns to certain aliens, such as those who apply for adjustment of status.
A-numbers may consist of 8 or 9 digits. The A-number is yours for life, much like a social security number.
From USCIS: Alien registration began in August 1940 as a program to record every non-citizen within the United States. The original Act of 1940 was a national security measure, and directed the former INS to fingerprint and register every alien age 14 and older within and entering the United States.
Also Known As: A-number, A#, Alien number, Green card number