Depending on how deep, and how long, it could take anywhere from 3 days to a week or more. If this scratch doesn't heal without an infection, then you should use peroxide on it, to clean it, then use some neosporin and a bandage on it. Hope this helps.
It depends on the severity of the scratch, and how fast you heal. It usually takes me about 2 days for a cat scratch to heal.
I would say a couple of days to a week at the most