An Intel Core i3 is what gaming is meant for. All i3, i5, and i7's are made for gaming. But there might be too many tasks running that's making your GHz slower? Or too many startup programs. Go to Computer>System Properties (It should be in a bar above everything else, with other options too), and just wait for the number it gives you. It's a number from 1-9...9 being the highest quality and performance that you have, and 1 being the lowest, basically crappy haha. But you should be fine.
-I even have a AMD processor with 1.60GHz and I play games just fine. Good luck though!