Sure, a cop CAN stop and search you here. More to the point, even if they couldn't, you wouldn't be able to stop them. The police have a lot less restrictions than US cops do. Do not fuck with the cops in Turkey, and do not carry anything you do not want them to find.
Warnings aside, it's highly unlikely that a cop will search a foreigner or get involved in any way with you, unless you are in a dangerous neighborhood or unless you acting crazy.
And as a last word of warning, the US consulate here is absolutely powerless. Do not rely on them to help you or to cover your ass if you are carrying something you shouldn't.