Paint iodine in the scratch wiht a fine brush and allow for it to dry. Start with a light shade first before applying more layers. For light-coloured wood, dilute iodine with an equal amount of denatured alcohol.
You can find iodine at pharmacies. If you would prefer another solution, Yumi offers several more in her info comic. Check out the full post over at Wonder How-To to learn more.
10 DIY Ways to Repair Nicks and Scratches on Wooden Furniture [Secret Tips from the Yumiverse]