When you say taxable income if you are taking that amount from line 15 of your form 1040, then yes you would file that tax return. If however, you mean income not including social security then generally no you would not need to file a tax return.
Generally, take 1/2 of your box 5 social security benefits and add that to your other gross income before any deductions. If that total is below $25,000 then none of your social security is taxable. That will exclude social security from your gross income. Now if your gross income excluding social social security is below the standard deduction for your filing status ($14,250), then generally you are not required to file a tax return for the year.
If your only source of income is social security then generally you will not need to file a tax return.
There are other special situations extracted from Publication 501 below where you must also file a tax return.
You must file a return if any of the conditions below apply.
1.You owe any special taxes reported on Schedule 2 (Form 1040), including any of the following (see the instructions for Schedule 2 (Form 1040)).
a. Alternative minimum tax.
b. Additional tax on a qualified plan, including an individual retirement arrangement (IRA), or other tax-favored account.
c. Social security or Medicare tax on tips you didn't report to your employer or on wages you received from an employer who didn't withhold these taxes.
d. Uncollected social security, Medicare, or railroad retirement tax on tips you reported to your employer or on group-term life insurance and additional taxes on health savings accounts.
e. Household employment taxes.
f. Recapture taxes.
2.You (or your spouse if filing jointly) received Archer MSA, Medicare Advantage MSA, or health savings account distributions.
3.You had net earnings from self-employment of at least $400.
4.You had wages of $108.28 or more from a church or qualified church-controlled organization that is exempt from employer social security and Medicare taxes.
5.Advance payments of the premium tax credit were made for you, your spouse, or a dependent who enrolled in coverage through the Health Insurance Marketplace. You or whoever enrolled you should have received Form(s) 1095-A showing the amount of the advance payments.
6.Advance payments of the health coverage tax credit were made for you, your spouse, or a dependent. You or whoever enrolled you should have received Form(s) 1099-H showing the amount of the advance payments.
7.You are required to include amounts in income under section 965 or you have a net tax liability under section 965 that you are paying in installments under section 965(h) or deferred by making an election under section 965(i).
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