Derek Muphy stated in one of his youtube videos (and I'm sorry, I can't remember which one), that what you can do is to first have someone follow you on Amazon. Then there's a way to sign up for promos. You can make it as simple as all they have to do is enter their email address to get a free copy.
However, I haven't done this myself yet because so far, all my books are free. (I use Smashwords, and all you have to do is send Amazon a single retailer link to get price matching. I sent them B&N. Don't bother sending Amazon the Smashwords link--they don't care.)
I was going to look into this for my next book, though. I'm planning on charging for that one, and it's a way to get free copies in the hands of my newsletter subscribers who are open to reviewing without futzing with prices for everyone else.
I'm going to have to go down the youtube rabbit hole to find the information again, though, since my second-hand recollection hardly seems sufficient. If you want to do it soon, I'm afraid that this is the only place I can send you to look. Derek Murphy does have sufficient tips to make the trip worthwhile, though, so it shouldn't be a waste of time, I hope.