Yes, if her only income is Social security, since you are providing more than half of her support, you can claim her as a dependent on your return. Claiming a parent means you would qualify for the $500 Other Dependent Credit which is a non refundable credit. This means, it can lower your tax liability by $500, but it will not lower it below $0.
Also, if you are not married, you could file as Head of Household. This could lower your taxable income.
If you find on your return that you benefit by claiming her, and your situation was the same in the last three years, you would be able to Amend Your Return to claim her for those years.
You are correct, she does not need to file a tax return since she has no income other than social security.
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