http://www.shipping-worldwide.com/car-exports.html
here is a list of RORO (roll on roll off) shipping routes.
after you find the two ports you want to use, you will need to start researching about availability of passanger cabions on these ships, and rules for driving your american car at your destination.
if you go, post a long vanity about your adventure.
I am planning to ride my Harley to Turkey, through Syria
and Jordan then back. Avoid Lebanon crazies and Israeli
border crossing stamps and 5 hour vehicle inspections.