Chanting is not typically part of an acupuncture treatment. Chanting is more typically a form of Tibetan Medicine.
This is not to say there are not acupuncturists who chant. Acupuncturists are an eclectic group and many of them have elected to study healing methods from many energy medicine traditions, including Tibetan medicine.
However, if chanting makes you uncomfortable, it should not be a problem to find a practitioner who just uses acupuncture and perhaps herbal medicine.