Can touching a genital wart with your finger cause a wart to form on finger ?

Genital Warts: Warts are contagious. The virus is easily spread by physical contact or even contact with sheets or towels. However, transmitting common warts from the hands to the genitals isn't likely at all since genital warts are a different strain from other warts, and transmitting genital warts to the hands is just as unlikely. All warts should be treated to avoid transmission, especially genital warts.