The 32 refugees asked police officers for help early Friday, Dogan news agency reported.
The group, which included six women and an infant, were taken to a hospital for examination and were expected to be transferred to a refugee camp.
The refugees said they arranged the boat trip from the beach in Antalya to Rhodes, 11 miles from the Turkish coast and more than 200 miles from mainland Greece. But the two men who had promised to take them never showed up.
Turkey is investigating traffickers who promise to guide refugees to Europe.