By becoming a citizen as soon as the law allows (5 years from becoming a permanent resident (3 years if you became a permanent resident through a marriage to a U.S. citizen and continue to be married to that U.S. citizen)), and then filing an immigrant petition for your mother.
While a permanent resident may apply for a green card for a spouse and unmarried child, you need to be a United States citizen to apply for a green card for your mother. Depending on how you obtained your permanent residence, you may be eligible to apply for US citizenship after two years and nine months of being a permanent resident.
You can't short of her getting a tourist visa. As a permanent resident you can only petition for your spouse or minor children. Once you become a citizen, you can petition for a change of status for your mother through an immediate relative visa.
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