According to the Social Security Administration's Legal requirements to provide your Social Security number, the following situations require it:
- Internal Revenue Service for tax returns and federal loans; Employers
- Employers for wage and tax reporting purposes;
- Employers enrolled in E-Verify;
- States for the school lunch program;
- Banks for monetary transactions;
- Veterans Administration as a hospital admission number; Department of
- Department of Labor for workers’ compensation;
- Department of Education for Student Loans;
- Loans; States to administer any tax, general public assistance, motor
- motor vehicle or drivers license law within its jurisdiction; States for
- States for child support enforcement;
- States for commercial drivers’ licenses;
- States for Food Stamps;
- States for Medicaid;
- States for Unemployment Compensation;
- Compensation; States for Temporary Assistance to Needy Families; or
- U.S. Treasury for U.S. Savings Bonds
None of those situations are "to apply for a position", which is the situation you are in. You may refuse to give it, and I personally would until I was actually signing a contract/offer letter/payroll papers for a specific company.
You might ask why your Social Security number is needed, how your number will be used, and what law they think requires you to give your number, if they push you on it, and determine you final answer from there.
As to your specific questions, I don't know how common it is -- I've not seen a request for a social security number in this context in a long, long time, but that is just me. It's quite possible that you are working with a dumb recruiter who thinks he or she needs/is entitled to this information; similarly, you could be working with a scammer.
As for your response being warranted, it's perfectly reasonable to ask to confirm if the position exists and if Recruiter X is handling it, and that's the extent to which I would discuss it with them.
