The cards were fitted to notify JRA when the traffic lights were faulty.
JRA believes a syndicate "with links on the inside" is behind the thefts.
"We have 2,000 major intersections in Johannesburg and only 600 of those were fitted with the cards," the agency's spokesperson Thulani Makhubela told the BBC.
"No-one apart from JAR and our supplier knows which intersections have that system."
The thieves ran up bills amounting to thousands of dollars by using the stolen cards to make calls.