You have a number of options when it comes to adding a gift wrap option in WooCommerce.
There are dedicated plugins specifically for gift wrapping in the WooCommerce Extensions marketplace – or you can use a more generic approach using “WooCommerce Product Add Ons” which can be used for other addons products, not just gift wrapping.
Gift Wrapper for WooCommerce
You can select not only to gift wrap individual products, but also the entire order.
Further to that, you can even offer up gift wrap designs / styles.
Check out Gift Wrapper for WooCommerce here in the official WooCommerce Extensions Marketplace
WooCommerce Product Add-ons
WooCommerce Product Add Ons can be used to offer gift wrapping and many other options.