Based on my experience it is 18", but I even heard that contractors don't like them this small. We recently changed all our 18" shafts on a job to 24" just based on a contractor's recommendation on constructibility.
When dealing with expansive soils, smaller is better, to reduce the uplift forces of the shaft side.
In Colorado I have seen thousand of residential projects with shafts of 8", 10" and 12". A lot of care is needed to construct these.
According to FHWA it can be as small as 12" but length should be limited to 8 to 10 feet. However, the document did not specify that a drill shaft cannot be less than 12". However, as a matter a practicality, I don't think it will be smaller.