Alex Rodriguez is fond of being seen smoking a cigar, but it is unclear as to whether he actually smokes cigarettes. My guess would be to say he doesn’t, since athletes don’t really maintain high levels of performance when they smoke cigarettes.
Smoking cigarettes and being an athlete don’t go together, unless you count pool or snooker as a sport. In that case they could. Alex Rodriguez certainly smokes cigars, though, that much is certain.