In order to change the gender marker on your Social Security Card you must,
1. Complete the application for a Social Security Card and attach one of these documents
A Driver's License or State ID with an updated gender marker.
A US Passport with an updated gender marker.
Legal name change order.
A letter from a licensed physician or psychologist certifying the individual has completed transition or is currently transitioning.
2. Submit the application and attachment in person or by mail to any Social Security Administration Office.