The protest near the Luilu plant follows the eviction last week of thousands of illegal miners from Glencore's Kamoto Copper Company (KCC) concession in southern Democratic Republic of Congo after 43 people died in a landslide.
The witness, a member of a local civil society organisation, said at least 50 protesters had gathered outside the plant to demand access to the nearby Mayi ya Mbata open cast mine, owned by the state company Gecamines.
In response, seven vehicles carrying soldiers arrived on the scene and attempted to disperse the crowd, he said.
Glencore said in a statement that about 80 people had protested on the national road in the town of Luilu. It said the army had dispersed the crowd and that no injuries had been reported.
Army and government officials did not respond to requests for comment.
The decision last week by the government to use the army to evict miners illegally digging on the KCC concession, which is majority-owned by a Glencore subsidiary, sparked angry protests outside the local governor's office and looting of shops last Thursday.
The government of Lualaba province, where KCC is located, has promised to provide other concessions where the evicted miners can dig, but they are sceptical that these will be sufficient to absorb them all.
Small-scale mining for copper and cobalt is one of the few viable economic activities available to much of the population. The miners use rudimentary tools to burrow dozens of metres below ground, leading to frequent accidents.
Activists say the deployment of the army to tackle the issue of illegal artisanal mining could lead to violence and human rights abuses, and have urged authorities to do more to address chronic poverty and unemployment.
Glencore said that, prior to last week's eviction, about 2,000 illegal miners were entering KCC every day. The Lualaba government estimates that 170,000 informal miners operate across the province.
(Reporting by Aaron Ross; Writing by Joe Bavier; Editing by Catherine Evans and Kevin Liffey)