If the supplier's product contains a Barcode (ISBN, UPC, GTIN, etc.), this field will be transferred to your store when the product is added.
If you don't see it listed on your end, the supplier likely does not have it listed in their Shopify.
You can always ask your partner if they have it available, using the contact information found in your Carro Partners tab.
NOTE: The Barcode field is not kept in sync and can be deleted by a Retailer at any time.