Need a ferry from istanbul to Dubrovnik
It'll probably never happen.
The only international ferry to Dubrovnik is the one from Bari, Italy.
I think it is doable, but a hassle. Take the ferry to Bari. From Bari to Greece. Greece to Turkey.
Go to www.seat61.com. Ferries and trains world-wide and how best to book them are detailed there.
As others have alluded, there is no direct ferry from Istanbul to Dubrovnik, and to take it further, no series of ferries that you could string together. The problem really starts with Istanbul, there really are no ferries at all from Istanbul into the Greek Isles, there are from several cities in Turkey to a nearby Greek island, but that is it. From any Greek Island, you can then get to Athens easily, but then you would need to go overland to Patras. At Patras, as was mentioned, you would need to go to Bari, Italy then to Dubrovnik. All in all, about 4-5 days of travel.