There are five main bases for people to get asylum - past persecution or a well-founded fear of future persecution on account of race, religion, nationality, membership in a particular social group, or political opinion.
It sounds like being persecuted for being a Kurd in Turkey might meet the legal definition of "race" or "particular social group."
However, this is a complicated legal question and it would be best to consult with an attorney regarding the details of your situation.
The facts you have provided are not sufficient to get a definitive answer on this issue. You'll be best served consulting an immigration attorney with any specific set of facts that you may have. Bear in mind that except for limited exceptions, asylum must be filed within 1 year of your last entry into the U.S. Good luck.
Political asylum applications must be decided on individual basis.
It is advisable to contact organizations that assist in the preparation of asylum application or retain an immgration lawyer to assist you.
Due to the fact of the severe consequences of frivolous asylum findings, it is imperative to have your asylum case assesed before application.
You are welcome to use the link provided below to contact me for a discussion.