If you are a U.S. citizen - yes, you can. However, it would make sense to check whether your parents are eligible for green cards before filing the petition. For example, if they are in the U.S. and have not been admitted, or if they are outside of the U.S. for less than 10 years after being in the U.S. for over a year illegally, or if they were ever deported, or if they entered the U.S. illegally more than once, then they would not receive a green card even through your petition for them would be approved.
Generally, any U.S. citizen age 21 or older may sponsor a parent in the application process to become a Lawful Permanent Resident (to get a "Green Card"); this is so regardless of whether the U.S. citizen is married or not. Of course, there are many other details that determine eligibility, and it would be wise for you and your parents to consult an immigration attorney who, after learning all of the relevant information about you and your parents would be able to advise about immigration eligibilities, options and strategies, and would be able to offer legal representation in the application process (which can be significantly more complex than it might first appear).
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