After enabling Artifact Registry, Run this command

 gcloud auth configure-docker

After creating a Repo in artifactory, use this command to build and upload to it:

 gcloud builds submit --tag $(GCR_HOST)/$(PROJECT_ID)/$(REPO)/$(SERVICE):latest .

Here’s my Makefile:

HOST := us-docker.pkg.dev
REGION := us-central1
PROJECT_ID := my-project
REPO := my-repo
SERVICE := my-service

include Makefile.env

all: gcp-setup cloud-build cloud-run-deploy

gcp-setup:
	gcloud config set project $(PROJECT_ID)

cloud-build:
	gcloud auth configure-docker $(HOST)
	gcloud builds submit --tag $(HOST)/$(PROJECT_ID)/$(REPO)/$(SERVICE):latest .


cloud-run-deploy:
	gcloud config set run/region $(REGION)
	gcloud run deploy $(SERVICE) --image $(HOST)/$(PROJECT_ID)/$(REPO)/$(SERVICE):latest