Yes you can sponsor your mother if you are a US citizen. However you should consider filing a waiver for your mother and even with the waiver because she is EWI, she may have to go to her country of origin to get readmitted legally. If you have however filed the waiver that will make things easier because then the embassy or consulate will not be able to deny adjustment and re entry based on the earlier illegal stay.
If she has nothing right now, she should do the Obama deferred action under the immigration reform, plus, a USA citizen can start the immigration process for their parents by filing a visa petition, etc.
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