This post assumes you're familiar with and using Python's logging module to log info from your script. If you don't care about how it works skip to the end to see the code for the full solution.
Our goal is to control the log level via the command line using an additional argument
--log_level that takes a one of the logging module's log levels.
$> script.py --log_level DEBUG
parsed_args = parser.parse_args()
root_logger = logging.getLogger()