I just had a son in may 2010 and my girlfriend who has lived with me for over nine years is collecting ssi $8,220 has no other income
Can I claim her as a dependent?

Yes, you can, if you provide more than HALF of her total support, which you probably do even with the $8,220 in SSI.

You can claim your g/f if she lived with you for all the year, did not earn more than $3650 (SSI is not counted as income) and you provided more than half of her support.