No Social Security does not count towards income.
See IRS Publication 501 starting on page 10 bottom Dependents
https://www.irs.gov/pub/irs-pdf/p501.pdf
Who can I claim as a dependent?
https://ttlc.intuit.com/community/credits-and-deductions/help/who-can-i-claim-as-my-dependent/00/267...
