I don't think it makes you smarter per se. If you don't move out of your comfort-zone, explore and educate yourself you probably won't get 'smarter'.
even as Tapas Adhikary calling it skilled is more accurate, still you can also get pretty skilled in doing things wrong.
I would go for something along the line:
Programming can help you to train abstract thinking and mathematical logic.
I do very strictly differentiate between programming, mathematics, engineering, physics.
programming is most of the time applied and based on the abstraction of the language and the task you want to solve and how you want to solve it makes a huge difference.
Assuming that programming makes you smarter, is like assuming that philosophy makes you smarter. Or psychology makes you more empathic. It's oversimplified in my opinion.