The RetroPie team took its time on purpose with this one and is still calling the support for the Pi 4 "beta," although it's now available for everyone and included within the 4.6 install.

"For RetroPie 4.6 we have moved to Raspbian Buster as a base for our pre-built Raspberry Pi images. Raspbian Stretch is no longer supported by Raspberry Pi Trading Ltd.

To install Retropie you need to download the image file from the downloads page and write it onto the microSD card. Note that there are two downloads, one for the Raspberry Pi Zero and original ...

The RetroPie team took its time on purpose with this one and is still calling the support for the Pi 4 "beta," although it's now available for everyone and included within the 4.6 install.