Quarshie is known for playing the roles of Sunda Kastagir in Highlander and Captain Panaka in Star Wars: The Phantom Menace. Quarshie appeared in the Doctor Who two-part episode "Daleks in Manhattan" and "Evolution of the Daleks" as Solomon, leader of the shantytown Hooverville, broadcast in April 2007. He also appeared at the Star Wars fan event Star Wars Celebration in 1999.
He also appears in the hospital drama series Holby City as Ric Griffin. He leads the cast of Michele Soavi's The Church as Father Gus and plays Aaron the Moor in the BBC Television Shakespeare Titus Andronicus.
Quarshie has narrated a number of television programmes, including the 2006 documentatary Mega Falls of Iguacu about the Iguaçu Falls, and the 2009 TV adaptation of Small Island. In 2010 he narrated the BBC Wildlife series Great Rift: Africa's wild heart. In September 2010 he appeared in an episode of Who Do You Think You Are?, tracing his Ghanaian and Dutch origins. The episode revealed that he traced his ancestry to Pieter Martinus Johannes Kamerling, a Dutch official on the Gold Coast, making him a distant relative to the late Antonie Kamerling, who was also an actor.