Google Cardboard appears to require a gyroscope to operate.
From: https://support.google.com/cardboard/answer/6295046?co=GENIE.Platform%3DAndroid&hl=en
Check phone requirements
Note: If you get a device incompatible message, you may not have a phone fitted with a gyroscope.
Using a gyroscope improves the orientation position of the handset so that turning your head to the left 45 degrees actually feels similar to a 45 degree turn rather than something else.
Note that if you want to view 360 degree video and are willing to deal with swiping/dragging on the screen to move around, that shouldn't require a gyroscope.
I believe there are various apps which will play 360 degree video/3D? without a gyroscope, YMMV.
If you really want to do VR/AR type behavior with your phone (in Cardboard or not) you are better off getting a phone with a gyroscope.
As ARCore is Google's AR platform, and they list supported devices here if you want to find something guaranteed to work.