The product description specifies it as a cleanser for the body and hands. Facial skin is generally more delicate and has different needs than body skin, so using a strong, traditional soap like this on your face carries a higher risk of irritation or over-drying.
If you're considering using it on your face, the same cautious testing protocol applies: try it on a small, less visible area first and monitor closely. Many people find tar soap too harsh for regular facial use, especially if they have dry or sensitive skin.
For hair, birch tar has traditional use in hair washing for its cleansing properties. However, this is a solid soap bar, not a liquid shampoo, which can be difficult to lather and distribute through hair, and may leave a residue. It's often considered a more involved, traditional method rather than a convenient daily hair wash. Always ensure thorough rinsing.