The Magento ® has a lot of different extnesion for gifting. But there no such good oppotunity to have promotional price rule where free gift product will be added with specific coupon code. The extension Coupon Gift Product allows to have this option.
With the coupon gift product extension you can make unlimited amount of protomitonals shopping cart rules and use different or same prodcuts as gift there. Also if you would like that gift product wasnt free you can also select this option by selection "Set Product Price to  0" to No. 
After saving rule you need to clear cache then you can check new promotional rule at the frontend. Once you will have something at the cart apply coupon code you created and you will see gift product in the cart.  You can preview demo video below: