The short answer is that if social security is your only income, it is not taxable and you do not have to pay quarterly taxes.
If you have other income, that will be taxable, and your social security may also become taxable. In that case, you either need withholding from your other income (like a pension or 401k), or you need withholding from social security, or you need to make estimated payments.
You can use this tool to estimate your tax bill and withholding needs.
https://www.irs.gov/individuals/tax-withholding-estimator
