Not if it's low enough.
No more tacky than telling someone about your designer clothing, the people you've dated, the fact that you were a cheerleader or football star in HS, or other things nobody really cares about.
Yes, I see no reason for it at all.
Yes, especially because of how uncommon IQ tests actually are and how worthless they are.
IQ was invented by French educators to predict whether boys, not girls, could do well in a specific French academy. They found that the highest score always went to the youngest boy in the class, but they insist that there is no way to prepare for the test or to improve your score. To this day they can not explain what exactly the test measures.
If you know your score it is certain that you took a wildcat version of the test, since genuine testers will not tell you what your score was. There are an awful lot of wildcat tests available because it's so easy for people to remember the questions and make up their own version later.
Unless you have a specific reason to do so, yes it's tacky.