If you’re in an airflow task, you can get the execution date, as a string, in the same format the API’s/etc use, like this:

def save_exec_date(filename, **context):

    with open(filename, 'w') as fp:
        fp.write(context["execution_date"].to_iso8601_string(extended=True))


save_exec_date = PythonOperator(
    task_id='save_exec_date_to_file',
    python_callable=save_exec_date,
    op_kwargs={
        'filename': exec_date.txt,
    },
    provide_context=True,
    dag=dag)