Assuming you are using the Azure Native provider package, the

identity

property is available in a newer ARM API version for container registry. For example,

import * as containerRegistry from "@pulumi/azure-native/containerregistry";

const acr = new containerRegistry.v20220201preview.Registry("containerReg", {
    identity: {
        type: "SystemAssigned"
    },
...
...
});

It might be available with earlier versions of the container registry ARM API too. Personally, I always check the most recent API version.

Winner! Thanks!