Ferries between Turkey's Mediterranean
coast and the port of Girne (Kyrenia)
in northern (Turkish) Cyprus are an on-again, off-again thing.
In summer 2014, service is scheduled to and from Taşucu,
the small port near Silifke,
east of Alanya and
west of Adana
on the Turkish Med coast. How it operates remains to be seen.
The current operator of the service is Akgünler Denizcilik, whose website may give you current information on the route and its services.
You can travel to/from both
Taşucu and Alanya by bus.
The nearest airport and train station
for Taşucu are at Adana.
the nearest airport is at Gazipaşa, southeast of Alanya on the way to Anamur.