well, it`s better to say I`m a Turk instead of I`m Turk, cause It`s a noun. but yea I think this needs a clarification from a native speaker.

 I would say he is arabic rather than he is an arab ....

I always say ´I am THE Turk´, instead of ´I am a Turk´

 But arabic here is an adjective,not noun,still you can use it this way ?

 As a ´native´ English speaker I agree with tamikidakika.

I´m a Turk is correct. (Not I´m Turk)

You can also say "I´m Turkish" and "I´m Arabian" or "I´m an Arab" (not I´m Arab).

You can say ´I´m psychic", so I think "I´m Arabic" is also acceptable English.

I must say that I am not entirely convinced with ´I am arabic´. You might be using it as a native speaker but I never heard of ´I am arabic´ but ´I am an arab´.

Dictionaries giving ´the inhabitants of Ireland and their descendants elsewhere´ for irish for example. And also turkish as ´Of or relating to Turkey or its peoples, languages, or cultures´ (some of them).

Maybe it is just easy and simpler to use in daily spoken  English.

It´s so strange how many aspects of your own language you just don´t consider till someone points it out to you 

I never really thought about it before, but yes we do not  make a distinction between the language and the nationality often.

I for example would never ask someone ..Are you a Turk ?, i would say, Are you Turkish ?.

I am spanish, I am german , I am arabic  etc etc

For some reason it sounds slightly rude to say..Are you an arab?, or are you a Turk ?...can´t explain why but it definitely is more polite to say Are you Turkish ?

 I agree with this

now the question is..... do you say arabian or arabic?. I have a work colleague who calls herself arabic so this would be my point of reference

 I don´t if it´s such a good idea........You just might find out that you are related to some people here

 Hey, are you my niece?