No. Social Security is a government benefit program. In order to be eligible for this benefit, you must waive your rights by accepting the assignment of a Social Security number. The number is property of the government, and having an SSN assigned to you represents acceptance of a government privilege.
If you want to be free from government control, you must rid yourself of government privileges, all of which require you to waive your God-given rights in order to obtain them.
When you give up your SSN, you also give up any benefits associated with that government program, as well as eligibility for most other government social programs (e.g. Medicare, unemployment insurance, Workmen’s Comp. etc.).
The trade-off is this: reclaim your freedom by giving up government-sponsored “security”, or accept government-sponsored “security” and give up your freedom. You cannot have both.