Can I petition my mom and how long would it take if I’m a 20 year old US citizen?

A U.S. citizen age 21 or older generally is able to sponsor a parent for immigration benefits with an application in the Immediate Relative visa category. Of course, there are many other details that impact eligibility. It would be wise for you and your mother to consult with an immigration attorney about eligibilities, options and strategies, and if applicable, steps that might be taken to become prepared for filing an application the moment you become 21 years old.