Yes you can. But washing your hair with soap will not feel the same as washing your hair with shampoo. Natural soap will clean your hair but it will leave your hair feeling slightly dry and waxy, especially if you have hard water. An acid rinse will take away the waxy feeling.
The acid rinse: add 2 tablespoons of apple cider vinegar (or white wine vinegar – the type in your kitchen) to a liter of water and rinsing your hair thoroughly after washing with soap. Adjust the ratio of vinegar to water if it’s not working for you. Don’t go beyond 4 tablespoons per liter of water.
If you don't like the concept of using an acid rinse then we make a 5% Sulfur & 2% Salicylic Acid shampoo bar. This is a non-soap bar that uses plant-based surfactant cleansing ingredients. It contains conditioners, detanglers, and vitamins to give your hair a softer feel. The surfactants don’t react with hard water like soaps.