You need to have Google Cloud Shell SDK installed on your local machine - https://cloud.google.com/sdk/docs/install
Open Google Cloud SDK Shell and type the below command.

gcloud auth application-default login

This will open up a browser where you can authenticate. The above command then create an ‘application_default_credentials.json’ credential file in the User Config Directory. You can find the config directory path using gcloud info. Look for the User Config Directory path.

You can use this to authenticate bigrquery by specifying the path to the credentials file.

library(bigrquery)
bigrquery::bq_auth(path="C:/~/gcloud/application_default_credentials.json")