I am 42 years. My father is a USA citizen. I came here on student visa. Can my father sponsor me for a green card?

Your father can petition for you as his adult child. However, since you are over the age of 21, you will not be considered an immediate relative and you will fall into a preference category. This can mean that you will have to wait a very long time for a visa to become available so that you can receive your green card.