No. Federal withholdings are voluntary.
Tax withholdings from your Social Security are not mandatory, but voluntary. You can request the Social Security Administration to withhold taxes by calling them or by filling out form W-4V.
Please read this SSA document for more information.
Taxes withheld from your Social security checks are then reported in Box 6 of your form SSA-1099.
When entering your form SSA-1099, remember to enter Box 6 - Voluntary Federal Income Tax Withheld and you will get credit for the taxes withheld.