It's true that the bacterium Propioni acnes is one factor linked to acne development. Reducing acne-causing bacteria can have a positive effect on your skin.
But antibacterial hand soap isn't great choice if you're looking for a facial cleanser to treat acne.
First off, antibacterial hand soaps are made for, well, your hands. The skin on your hands can generally tolerate stronger cleansers than can the delicate skin on your face. Using hand soap on the face can easily over-dry and irritate your skin.
Secondly, bacteria is only one piece of the acne-causing puzzle. There are other factors at work too -- hormones, abnormal shedding of skin cells, overactive sebaceous glands, development of comedones, to name a few. Antibacterial soap isn't going to do anything to treat these acne causes.
If you're keen on using an antibacterial soap to treat facial acne, choose one that is specifically made for the face. Triclosan, the active ingredient found in most antibacterial hand soaps, is incorporated into some brands of acne facial cleansers.
You can also choose an acne cleanser that contains benzoyl peroxide. Benzoyl peroxide not only will help reduce bacteria, but can also reduce oiliness and keep pores from becoming plugged.
You needn't spent a lot of money on an acne cleanser either. A drugstore brand can work just as well as a fancy salon product.
So keep the hand soap for your hands. There are better antibacterial cleansing options for your face.
Choi YS, Suh HS, Yoon MY, Min SU, Kim JS, Jung JY, Lee DH, Suh DH. "A study of the efficacy of cleanser for acne vulgaris." J Dermatolog Treat. 2010 May; 21(3):201-5.
United States. NIAMS. "Questions and Answers About Acne." Bethesda, MD: National Institutes of Health, 2006.