One of the requirements is to reside in the United States for five years before applying for citizenship. Because you never lived in the United States, I don't think you can apply for a U.S. citizenship.
To be able to apply for US citizenship, you must first be a legal permanent resident for at least five years and reside in the US for the majority of those five years.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
Your son needs to petition for you to become an LPR. Once you held that status for five years in the United States, you will be able to seek citizenship, which, the way I see your facts, is not really what you are asking about. LPR status will allow you to live in the USA and you will be able to get your immigrant visa to come to live here within a year or so of your son's application filing date.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: firstname.lastname@example.org; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.