Yes - an alien individual eligible to be claimed as a dependent on a U.S. federal tax return, but who isn’t eligible to get an SSN may be claimed after filing form W-7, Application for ITIN. However, an ITIN doesn't qualify a dependent for Earned Income Tax Credit purposes. You should complete Form W-7 as soon as you are ready to file your federal income tax return, since you need to attach the return to your application. Access the form here: https://www.irs.gov/uac/about-form-w7