I didn't get 3 months free subscription when bought a new iPhone 12 mini

Hi SiMoon82,

Thanks for coming to Apple Support Communities for help today. It sounds like you aren't able to get the free Apple Arcade trial after you new iPhone purchase.

Have a look here: Apple Arcade - Three Month Offer.

"You can start your free 3 month subscription to Apple Arcade after setting up your new Apple device. Here’s how to redeem your offer:

1. Turn on your new Apple device and sign in with your Apple ID.
2. Open the App Store. Tap or click Apple Arcade. And make sure your device is running the latest version of iOS, iPadOS, tvOS, or macOS.
3. The offer should be presented immediately.
4. Choose "Get 3 Months Free."

If you still aren't able to redeem the offer, please visit Get Support.

Have a fantastic day!