In Saturday's third round, Aiken's 4-under 69 helped him catch Fisher, who has held at least a piece of the lead in all three rounds at the European Tour tournament.
Fisher managed a 2-under 71 Saturday, while Aiken parred the 18th after three straight birdies pulled him into a share of the lead at the East London Golf Club in East London, South Africa.
"I haven't won a main tour event yet, so that would be a nice thing to get under my belt," Aiken said. "It's something I've been looking to do for a while now."
South Africa's Jbe' Kruger (67) is 15-under 204, alone in third place, while South Africans Carl Schwartzel (68) and Jake Roos (66) share fourth at 14-under 205.