When I put the key in the ignition and turn it to turn on the car as the car is starting the steering wheel shakes but then stops once the car is on
My car has 55600 miles.
My car has an automatic transmission.
Depending on the model of Camry you have, you may have an electrical steering system in the vehicle. The steering goes through a test when you first start the car and calibrates the steering system.
If you feel like what you experienced was not normal, and the steering has never acted that way before, then you may need to have the system checked. I do not find any recalls or bulletins for this problem and have never seen the issue myself. I would recommend having the system checked as soon as possible as it may be a prelude to a steering problem or failure.
If you decide to get this fixed, enlist a qualified technician who can diagnose the issue with your steering wheel and perform any repairs that are necessary.