No, your dog can definitely not eat acorns. Acorns contain tannins, which can be fatal to your dog.
Going Nuts for Acorns
So while you are outside, you will need to teach your best friend how to avoid acorns. You might try catching them in the act with a firm “no”. There are many techniques to use. And in the beginning, you will have to be hyper-aware of what your dog is doing with her/his nose down in the grass.