You cannot sponsor a relative to become a U.S. citizen directly. Instead you can sponsor them to become a permanent resident and later, if they qualify, they can apply for citizenship. As a part of the process, you will have to submit the I-864, Affidavit of Support, which is an undertaking to support your relative financially when in the U.S.
Eligibility to become a sponsor:
Citizenship Application Form N-400
Replace Certificate of Citizenship Form N-565
Certificate of Citizenship Form N-600
Green Card Replacement Form I-90
Remove Condition on Green Card Form I-751
Adjustment of Status Form I-485
Visitor Exchange Visa (J1 Visa)
Skilled/Unskilled Work Visa (H2B Visa)
Intracompany Transferee (L1 Visa)
Extraordinary Ability Work Visa (O1 Visa)
Religious Worker Visa (R1 Visa)
US Visa Entry for Spouse and Children
US Citizenship Application Form N-400
Employment Authorization Document Form I-765
Travel Document Application Form I-131
Conditional Green Card Form I-751
Certificate of Citizenship Replacment Form N-565
Certificate of Citizenship Application Form N-600
Duplication Approval Notice Form I-824
Affidavit of Support Form I-134
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