From this paper.
Arthropological evidence suggests that hunter-gatherers consumed sorghum as early as 8000 BC (Smith and Frederiksen, 2000). The domestication of sorghum has its origins in Ethiopia and surrounding countries, commencing around 4000–3000 BC. Numerous varieties of sorghum were created through the practice of disruptive selection, whereby selection for more than one level of a particular character within a population occurs (Doggett, 1970). This results from a balance of farmer selection for cultivated traits and natural selection for wild characteristics, generating both improved sorghum types, wild types and intermediate types (Doggett, 1970). These improved sorghum types were spread via the movement of people and trade routes into other regions of Africa, India (approx. 1500–1000 BC), the Middle East (approx. 900–700 BC) and eventually into the Far East (approx. AD 400). By the time sorghum was transported to America during the late 1800s to early 1900s, the diversity of new sorghum types, varieties and races created through the movement of people, disruptive selection, geographic isolation and recombination of these types in different environments would have been large (Wright, 1931; Doggett, 1970).
This would date the domestication of sorghum to roughly the same era that the Neolithic arrived in east Africa, about 6,000 years ago, and would seem to be a secondary domesticate. There is a mention in a Wendorf ? article that lipids in a sorghum pot from el Nabta were more like domesticated Sorghum..
Radiocarbon dates place the El Nabta sites between 8,100 and 7,900 B.P. One of these, E-75-6, is much larger than the others and consists of a series of shallow, oval hut floors at–ranged in two, possibly three, parallel lines. Beside each house was one or more bell-shaped storage pits; nearby were several deep (2.5 m) and shallow (1.5 m) water-wells. This site, located near the bottom of a large basin, was flooded by the summer rains. The houses were repeatedly used, probably during harvests in fall and winter Several thousand remains of edible plants have been recovered from these house floors. They include seeds, fruits, and tubers representing 44 different kinds of plants, including sorghum and millets. All of the plants are morphologically wild, but chemical analysis by infrared spectroscopy of the lipids in the sorghum indicates that this plant may have been cultivated. Of the four El Nabta sites that have yielded fauna, two contained bones of a large bovid identified as Bos. The faunal samples from the other two sites are very small.
But it’s not exactly conclusive.
There’s a book reference here for sorghum.