I checked several online sources, and her birth date is not given in any of them. Apparently no one knows.
http://www.newadvent.org/cathen/09730a.htm
To find out the year and date of St. Martina's birth, you can either search online or consult historical records, books, or articles about her. St. Martina is recognized as a Roman martyr, and as such, her historical information may be limited or uncertain. However, with some research, you may be able to find the desired information about her birth.
