Can and should are two very different words when it comes to this question. Simply put, you CAN wear whatever you want when you are in Istanbul and nobody will say anything. We were in Turkey for 3 weeks earlier this year and spent 6 days in Turkey. You will see tourists, especially female tourists, wearing super short shorts or skirts or shirts that could pass for rags as well.
What you SHOULD do is be respective of the local Muslim culture. Not just in Istanbul but any Muslim country. Wearing shorts or skirts that cover your knees or at least get close to the top of your knees is recommended. Carry a scarf to use when visiting places too, specifically mosques. When visiting mosques, they will often provide wraps for people who are underdressed,but who knows how often those are cleaned, do you really want them touching you.
So the key is to be smart and respect the local culture and you're fine over 6 years ago
Ipadnomads (again!) has great advice.
Skirts are fine in Istanbul - but not tight, and not short. If your knees (and elbows) are covered, you should be fine.
When I was in Istanbul a young woman walked by wearing a very tight skirt and top, and a local guy cat called etc .... She turned on him and started yelling at him in Turkish .... It was clear she was telling him where to go, that she was no tourist, but a Turk too.
So, regardless of whether you're local or not, you can wear what you want ... But you might get a reaction.
Turkey is a fantastic place to travel though - my favourite country. Here are some tips: http://traveleater.wordpress.com/turkey-field-notes/ over 6 years ago