A Fiat-Chrysler investigation found that certain trucks may have steering-wheel wiring harnesses that wear because of contact with a spring.
"Such wear may cause a short-circuit that may lead to inadvertent driver-side airbag deployment," the company said in a statement.
The National Highway Traffic Safety Administration said the problem could increase the risk of injury.
The automaker said it is aware of two related injuries, but no accidents.
"An analysis of warranty data linked to steering-wheel wiring harnesses determined less than one percent of all such repairs involved inadvertent airbag deployment," it noted.
An estimated 1.06 million of the trucks are in the U.S. The rest are in Canada, Mexico and outside the NAFTA region.
Drivers may be alerted to the problem by illumination of the airbag warning light in some of the trucks.
Ram dealers will tie back the wiring harness and install protective caps on the airbag retainer spring ends. The recall has started. Owners can contact Fiat-Chrysler customer service at 1-800-853-1403.
Edmunds says: Notices are being mailed now to advise affected owners when they may schedule a service appointment with their dealers.