In general, yes, and it can certainly help keep you from getting “less smart”, meaning exercise has been shown to be the most powerful anti-aging tool for preserving or improving brain function. Exercise improves brain health much like it does for other parts of the body. It increases the growth of brain cells and blood vessels while reducing damaging inflammation. All these brain exercise induced factors work to improve learning and memory, delay age-related cognitive decline, reduce risk of neurodegeneration (brain cells declining) and plays a role in alleviating or staving off depression.
One of the most famous research projects regarding exercise and intelligence came out of the Naperville Ill. school system where students were put into “Zero Hour” Physical Education (P.E.) to determine whether working out (high intensity fitness workouts, not sports or “standard P.E.”) before school would give kids a boost in learning compared to kids that did standard P.E. later in the day. The answer was yes. The students in Zero Hour scored better in almost all areas of learning and reading. Exercise clearly heightened their senses, focus, improved moods and they were all more motivated and invigorated to participate in class compared to the other group.
So yes, in many ways for the old and young, exercise can make and/or keep you smarter.