To a degree, yes, but soap needs to be basic to remain soap. I wouldn’t recommend it as the more acidic soap is, the less effective it is.
To recap: soap is a reaction between fats and a strong base (something like sodium hydroxide [NaOH] or potassium hydroxide [KOH]—typically called “lye”). The end product is basic, typically with a pH around 9.
The basic pH of soap is an integral part of its soap-ness. When soap becomes acidic is ceases to be soap and instead transforms into free fatty acids. The lower the pH of the soap, the less it suds, as more and more of it ceases to be soap.
Kevin Dunn has been running an acidic soap challenge for a few years now, and has yet to receive a successful entry. I had an interesting talk with him at the 2018 HBBG conference in Toronto. He described an experiment where one can add acid to a soap solution and watch the fatty acids precipitate out of solution. One can then add some NaOH solution and the mixture will suds again!
If you want to make an acidic (or even just more acidic) cleanser, I’d recommend shifting to working with surfactants. Lowering the pH of soap also lowers its efficacy as the addition of acid slowly eliminates the soap from the mixture.
Posted in: Soap