Yes. Section 13 of the INA allows it. You must show that you entered the United States as an A-1 or A-2; duties were diplomatic or semi-diplomatic in nature; there is a compelling reason why you or your immediate family cannot return to the country which accredited you as a diplomat; you are a person of good moral character; you are admissible to the United States for permanent residence; and granting you a green card would be in the national interest of the United States. While applying for adjustment of status, you must submit Form I-566 (Interagency Record of Request) and Form I-508 (Waiver of Rights, Privileges, Exemptions, and Immunities).