Yes, they can ask for that. Employers are required to have documentation as to the status of their employees.
This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Laws vary widely from state to state. You should rely only on the advice given to you during a personal consultation by a local attorney who is thoroughly familiar with state laws and the area of practice in which your concern lies.
The Dept. of Homeland Security requires all employers to verify identity and eligibility for employment by using a Form I-9. A passport satisfies both requirements. A driver's license satisfies identity. A Social Security Card or a Birth Certificate satisfies employment authorization.
In other words, they are entitled to see your birth certificate or social security card as a condition of employment. If they do not have a completed I-9 in your personnel file they are in violation of the law.
The response given is not intended to create, nor does it create an ongoing duty to respond to questions. The response does not form an attorney-client relationship, nor is it intended to be anything other than the educated opinion of the author. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change. Attorney is licensed to practice law only in the State of California. Responses are based solely on California law unless stated otherwise.