Yes, you can select whether to offer a specific product with free shipping when adding it to Etsy, as shown below.
As part of the flow, simply select the checkbox next to Display with free shipping on your storefront.
Note: Although you are displaying the product with free shipping, you'll still need to cover the shipping cost when fulfilling the product, so we recommend that you add the cost for shipping into your product price.
IMPORTANT: In some rare cases, if the only available method will be Express shipping, your customer will still see free shipping in your store, while you as the store owner will cover the cost.