Do you find the way to do it ? Or still
First we need to define what an internship is in Turkey. Internship unlike USA or other countries is the last year of medical school in Turkey. To do an internship is not a requirement to get a residency position, so if you are looking to get into a Turkish residency you don't need to bother doing an internship or trying to have an hands-on experience in Turkish Healthcare System. That being said, if you are just looking for an 2-3 months of experience of hands-on clerkship in Turkey, there are several ways of doing it.
1- IFMSA has exchange rotations that are held yearly and every country has their own chapter, you can contact your countries IFMSA chapter to see if they have any available exchange with Turkey
2- If you are from European Union countries, you can arrange a 4-6 months of exchange via Erasmus student exchange program.
3- You can contact individual schools about their own requirements, but personally I haven't seen any one other than those two options did some part of internship in Turkey (This is coming from someone who is in a prominent school)
For those interested in Residency;
Unlike US or other countries, there are no interviews in Turkey and getting into the residency in Turkey is quite simple. Turkish Medical Examination (a.k.a TUS) is held twice every year one in February, other in August. All you have to do is to register in this exam and get the highest score possible. If theoretically you got the highest score, you can be whatever you want plastic surgeon/dermatologist etc. thus for those asking what to do to increase your chance is plain STUDY for that exam. Turkey has amazing opportunities for foreign-trained doctors as unlike nearly all the countries, foreign people got into same spots with significantly lesser scores thus it is really easy if you want to be a <put highly competitive specialty here>. However, it comes with its own caviat, as per Turkish law foreign doctors can't be paid through the government and the only pay that they got is call pay & hospital revenue pay which ranges around 3500TL for call/workload intensive specialties and 2000TL for chill specialties.
That being said, foreign people have their own slots in Turkey. So if the university/hospital that you desire do not have an open slot for that specific TUS that you are taking you can't get into that spot. You can't apply for the spots that are designated for Turkish people but again this is not a problem as our beloved system only opens highly competitive specialties in better hospitals for foreign people. Slots are announced 1-2 months prior to that exam period (For February around January etc.)
Regarding TUS: It is a tough exam that heavily depends on memorization. There are specific courses like Kaplan in Turkey where people enroll throughout the year and use their resource. Exam is in Turkish, but you don't need to be fluent in Turkish. All you need is to score high in that exam. If you can read/understand in Turkish and get the exam done that's fine by all means for getting into residency. We had plenty of residents who barely speak Turkish and somehow survived.
All in all: If you are interested in Turkey, and would be fine living with moderate amount of money in Turkey (I would highly suggest you to do residency in Turkey as it is very easy and straightforward for foreign people). You would be making decent amount of money post-residency (private hospitals around 10.000TL/month depending on specialty -I know this is debatable- and can stay/get citizenship relatively easily compared to other European countries.
Hit me up if you have additional questions!