Can a file a petition for my unmarried 32 years old son, who came to us 10 years ago with a visitor visa and overstayed in the US? I am a us citizen

You can file a petition at any time. But that's only the beginning. To get a green card he needs to either do Adjustment of Status (AOS) in the U.S. or Consular Processing (CP) abroad.

He is not eligible to do AOS, because for people in non-Immediate Relative categories (Immediate Relatives include spouses, children under 21, and parents of U.S. citizens; your child is in the F1 category, unmarried adult children of U.S. citizens), they must be in status at the time of filing for Adjustment of Status. He is not in status, so this is impossible.

Doing Consular Processing requires going to a U.S. consulate abroad. The problem with that is that if he leaves the U.S. he will trigger a 10-year ban for accruing at least 1 year of unlawful presence and then leaving. That means he cannot come back for 10 years. He can try to get a waiver of the ban based on hardship to you, where he files I-601 at the consulate when he applies for an immigrant visa. Currently, he cannot apply for a provisional waiver (I-601A) before he leaves the U.S. unless he has a spouse or under-21 child who is a U.S. citizen; but this is announced to change in a few months. In a few months, he should be able to file I-601A to see if he can get a waiver; and if he can, there is a good chance that he can get a green card through Consular Processing smoothly.

If he can't get a waiver, there is no easy way for him to get a green card without spending a long time outside the U.S. -- unless he marries a U.S. citizen.