James was one of a gang of 15 robbers who stole £2.6 million ($4.5m) from a Royal Mail Train during its run between Glasgow and London in 1963.
Rapley said James used to race in the Brabham BT2 before going to jail for the robbery.
Rapley has owned the car since the 80s and regularly races in it himself.
He said other notable racers who had driven the car included Graham McRae and Denny Hulme.
"It's part of New Zealand history and I'm really only the present caretaker of it," he said.
Whether the thief was trying to steal the car or simply the caravan it was housed in was "the $64,000 question".
"What were they after? They certainly cut the chain and took it away during the night, which wasn't very nice of them.
"I'm quite worried as to what they took and why they took it - are they going to trash the bit they don't want?
"It's really a very puzzling situation."
The car would be impossible to flog on Trade Me, but Rapley held a fear the thieves might try to sneak it out of the country to be sold for parts.
"I've had it for a long time, I look after it myself," he said.
He asked that the thieves leave the car somewhere it could be collected, rather than wreck it.
He said the car could be worth anywhere between $50-100k, and the caravan would be about $12k.
Rapley said he was "really intrigued".
"Please drop it back."
