I found a picture of this tower, naming it Fındık Burcu. It is on Google Maps under a slightly wrong name.
A sight says "It is right next to Leblebi Kıran Burcu between Mardin Gate and Yeni Gate.

It is written in its [foundational] inscription that it was built by the architect Selame's son Muhammed upon the order of Ebu'l Feth Melikşah, the son of Seljuk ruler Alpaslan. It is said that it took its name from its round shape that took up little space. There is an inscription on the bastion."