About a week ago I had a lot of build up from co-washing with oily conditioners, and since I had decided not to use shampoo, I thought baking soda would be a good option. However, it seeped onto my forehead and really irritated it. I would never use it on my face on purpose for this reason. Like a fellow curly already responded, it is extremely alkaline and skin is naturally slightly acidic.
I recommend just exfoliating with a cloth. Oils can clean faces very well, and they are so moisturizing! Just be sure to avoid mineral oil, which is pore-clogging and not an organic substance. My favorite is unprocessed coconut oil. You can cleanse with it and rub it off, then add more as a moisturizer.