If it wont take a photo when AF is enabled, it usually means the camera is in focus-priority mode ("One Shot" AF) and the camera is unable to confirm focus.
The most common reason for this is a lens failure -- usually the auto-focus motor is no longer working. It could be a camera fault... that's just not very common. The easiest way to confirm the camera is fine (and determine if the issue really is with the lens) is to try a different lens.
If this is the "kit" lens that came with the camera (the EF-S 18-55mm f/3.5-5.6 IS) then it's not worth repairing because the cost of labor will quickly exceed the value of the lens.
If that is the case (and it probably is), then you could use the opportunity to get a better lens. The 18-55 kit lens now comes in a version with STM motors (and that version has improved optics). But there are also several lens options if you want a bit more zoom range or better focal ratios, etc.
But before you do anything, you'd want to confirm that the inability to take shots in AF mode really is isolated to your current lens and not the camera body (it's very unusual for it to a problem with the camera body... but I'd make certain of this before spending any money on replacing the lens.)
07/31/2023: New firmware updates are available.
05/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
04/20/2023: New firmware version 1.4.1 is available for EOS R3
03/30/2023: New firmware updates are available.
2/07/2023: New product announcements!EOS R8 EOS R50RF-S55-210mm F5-7.1 IS STMRF24-50mm F4.5-6.3 IS STMRF15-30mm F4.5-6.3 IS STM