If you are a permanent resident of the United States – i.e., hold a green card – you can become a U.S. Citizen through naturalization. There are several requirements – with some flexibility – to get naturalized.
To become naturalized you must have lived in the country as a permanent resident for five years, you have been physically present in the U.S. for at least half of that time, you are a person of good character, you have basic knowledge of U.S. history and government, you can read, write, and speak basic English, you are 18, legally competent, and you express your allegiance to the United States.
Also, if you were required to file a tax return while in the United States, and did not, you will be denied citizenship status.