How can I access the low level psycopg2 connection in Django?

You can see from the source that from django.db import connection returns a DatabaseWrapper for the default DB. In the psycopg2 backend you'll see that the DatabaseWrapper accesses the low level connection via connection.cursor().connection.

Those answers are good but not copypastable and with outdated docs so let me fix that.
As of version 3 you use the raw connection like that

from django.db import connection

stmt = "SELECT * FROM foo"

with connection.cursor() as cursor:
    cursor.execute(stmt)