A torque control apparatus and method for a drive motor is provided. The torque control method includes determining whether an input request torque is a rising torque or a falling torque. In addition, a controller is configured to select one of a rising rate map and a falling rate map based on a result of the judgment on the input request torque. Further, the controller is configured to adjust a rising rate of the rising torque using the rising rate map or a falling rate of the falling torque using the falling rate map.