Yes, fleas can bite your face but it is less common than other areas of the body.
Flea bites are most commonly associated with lower body areas such as the feet, ankles, and legs. This is because those are the closest access point for fleas residing on the ground to jump to.
The next most common location on the body for flea bites is around the midsection, as fleas commonly attach themselves to the waistline of clothing and then bite the open skin in that area. This may result in a linear line of flea bites around the waistline of the clothing.
But fleas can also bite on the face, although it is less common. This may happen if the bedding material or linen that that person is using is infested with fleas. When the person lays down to sleep, his face is within easy access of the fleas which results in multiple flea bites.