Go back to the store you got it from and talk to them while it is still under warranty.
Are you sure it is really turned OFF, before it turns itself on?
Do you mean when the camera is sitting untouched it turns on without touching it?
If the camera is only asleep, it will turn on when touching the shutter button.
Camera is sitting on table next to me as I'm reading. I hear "ding", and look over to see LCD screen lit up and showing last pic I took...from two days ago. Happened more than once. I spoke with Canon tech yesterday and camera is on its way back for service. I bought it in early June and have only used it a few times inside the house to "practice." I'm a novice.
I'm sorry to hear your camera is powering itself on. If you have a second battery we would recommend loading that in the camera to check if the same thing happens. If the issue continues with a different battery, or you don't have a second battery to test with, we would recommend sending the camera in for service. If you send it in make sure to include a copy of the proof of purchase in the box. The technician will need that to verify the warranty.
The Canon U.S.A., Inc. online repair portal allows you to set up service in a few simple steps. The repair portal gives you the ability to set up service for multiple pieces of equipment at once, and to receive a repair estimate in the majority of cases, depending on your model and issue. The portal also allows you to upload images or videos that will assist us in repairing your product. You can also select how you wish to be notified of the progress of your repair. The portal's service history section allows you to view all services that have been performed on any of your camera or video products since January 7, 2020.
Please follow the link below to access our online repair portal to arrange for service:
Instructions for Accessing and Using the Online Repair Portal
You will need to access or create your My Canon Account.
If you already have a My Canon Account and your product is already registered, simply click on the “Get Repair Services” link on the left menu and follow the onscreen instructions to arrange for service for your product.
If you have a My Canon Account and your product is not registered, you must register your product first. Click on the “Get Repair Services” link on the left menu, then click on the “Register Product” link on the right. After your product is registered, click on the “Get Repair Service” link on the left menu and follow the onscreen instructions to arrange for service for your product.
If you do not have a My Canon Account, you will need to create one. After you create your account, click on the “Add Product” link to register your first product. After your product is registered, click on the “Get Repair Service” link on the left menu and follow the onscreen instructions to arrange for service for your product.
Once you have completed the repair request, you will have an opportunity to print a copy of the request for your records. This request form will also contain shipping instructions and an address label that you will attach to the outside of your shipping box when mailing your equipment for repair.
UPDATE: I just received "a" camera back from Canon. It was sitting outside my garage door. I never got any emails saying it had shipped or had arrived. Good thing I was home.
Letter inside: "Since repairs are not performed on the camera model you sent for repair, we have shipped a new or factory-refurbished product to you in exchange for your original unit."
I just bought the camera last month at Best Buy for more than $700. Now, I have what might be a factory-refurbished model in its place. Canon did include another battery, battery-pack and wrist-strap.