Melt the tallow, beeswax, coconut oil, and shea butter together in a double boiler over low heat. Once everything is fully melted, remove the mixture from heat.
Stir in the arrowroot powder and baking soda, mixing thoroughly so there are no clumps.
Allow the mixture to cool slightly, then add the essential oils if you are using them.
Pour the mixture into small jars or deodorant containers and allow it to set completely at room temperature. As it cools, the deodorant will firm up and become smooth and solid.