Not all of them, unless you are calling the Tourism Police in Sultanahmet. Those in the office can speak English, German, French, and Arabic. It is located between Hagia Sophia and Basilica Cistern.
The address is Yerebatan Caddesi 6, Sultanahmet. Phone: +90 212 527 4503
Other than that, the younger cops in Istanbul are mostly college graduates, and will most likely be able to communicate with you in English. There is a special department called Yunuslar "Dolphins", which mostly speak English. They have a slightly different uniforms, and mostly ride on motorcycles.
