Перевод - Турецкий-Английский - merhaba seninle tanışmak istiyorum güzeliyinden...

Hello turkishmiss, if he wants to "görüşmek", it's ok. But he wants to "tanışmak" in other words "birbirlerini tanımak". This means "to be acquainted with each other".
So, I think it's better like this: "I want to get acquainted with you." or "I want to make your acquaintance."

for me "to meet" is o.k. Because there is nothing for "birbirini tanımak=to be acquainted with each other"in original.

Merdogan bey, ben yabancı olduğum için emin olamıyorum ama, Türk erkekler için bir kız ile "tanışmak" "meet"ten daha samimi ve yakın olmak anlamına gelmez mi? Yani en az kişliğini bilmek istiyor. Ne dersiniz?

Hi cesur,

May I ask you again to make your comments in English please?

you can find tanismak here, it seems that it means both "to meet" and "to get acquainted".

I'm so sorry. I would like to explain like this; In this case, he has met her before, because he knows her beauty. So he wants to know more about her. He wants to become acquainted with her (as a man).

cesur,

What makes you think that he knows her or they have already met?
He may be impressed by her beauty in a photograph or through the internet.