Use "do" and you'll be understood. It's grammatically correct, but not the most idiomatic way of saying it. We just don't often hear it that way, so people will think your English is pretty good, but that you still need to improve a little!
I think it's perfectly normal to say "do a sport". I've often heard the question asked "do you do any sports?" Remember, not every sport is played (i.e. surfing, skating, skiing, rock climbing, et cetera).
I would say that you should use the verb form of the activity if there is one.
Do you surf? Do you ski?
Otherwise use play.
Do you play football? Do you play tennis?
As mentioned above, there are situations where the activity has no convenient verb form or is not game-like (is not "played"), and neither of the two formulas above can b