Yes, there are black people in Istanbul. Istanbul is a cosmopolitan metropolis, and is getting more so each year- you can find nearly every type of person here. That being said, there tends to be a bit of racism against blacks here. Many Turks will assume that if you are black you are a poor refugee from Africa, due to the country's placement on the borders of the E.U. For the traveler, this means that unless you are in Beyoglu or the touristy parts of the city, this means that people may be suspicious or questioning. For more information, check out this excellent thinkpiece written by an Istanbul Expat:
http://istanbul-en.ihollaback.org/2011/08/18/zenci-sje/