Yes, any PC gamepad with analog sticks will work with iRacing.

First you'll need to plug the controller in to your PC via USB or USB dongle + wireless, install the drivers if need be, and you're good to go.

Then in iRacing you calibrate it as you would a wheel. Follow the onscreen instructions and move move the stick left and right when it asks you to calibrate steering... push down the triggers for gas and brake calibration, etc.

When calibrating the steering, make sure to select "Device is a joystick/gamepad"

The Joystick does not provide as much precision or feedback as a steering wheel, but you can stabilize your thumb by pushing the stick you steer with all the way forward when driving to help you be less twitchy. 

NOTE: iRacing does not use Steam's controller integration. If you are trying to use iRacing with a Playstation controller, you must setup DS4Windows using the instructions at