Scotty, i have a 2002 Avalon with 130k on it. The car pulls to the left and I have had it aligned 4 times by two different places. I replace the left inner and outer tie rods and tires. Still pulls. Brakes have been checked also. It doesn’t matter if it’s accelerating or not, still pulls left. Could it be the rack?
try switching your 2 front tires....if it pulls to the right after the switch, you may have a problem with your tires.
You said you got new tires...It might be tire conicity. Happens with new tires when there's a mfg. defect.
Wheel conicity is a defect in the tire caused by faulty manufacturing. This happens when the belts under a tire’s tread aren’t perfectly aligned, causing it to inflate into a cone-like shape. New tires are usually where this problem can be found,
I located a Toyota T-SB: Vehicle Pulling to One Side
https://attachments.priuschat.com/attachment-files/2015/10/96272_T-SB-0391-08.pdf
It's a comprehensive repair manual for a number of Toyota's with the issue you are describing (2002 Avalon is included).
