diff --git a/django/db/backends/postgresql/base.py b/django/db/backends/postgresql/base.py
index 3db3d6abd2..5ed856448f 100644
--- a/django/db/backends/postgresql/base.py
+++ b/django/db/backends/postgresql/base.py
@@ -223,7 +223,13 @@ class DatabaseWrapper(BaseDatabaseWrapper):
 
         conn_params.pop("assume_role", None)
         conn_params.pop("isolation_level", None)
-        conn_params.pop("server_side_binding", None)
+        server_side_binding = conn_params.pop("server_side_binding", None)
+        conn_params.setdefault(
+            "cursor_factory",
+            ServerBindingCursor
+            if is_psycopg3 and server_side_binding is True
+            else Cursor,
+        )
         if settings_dict["USER"]:
             conn_params["user"] = settings_dict["USER"]
         if settings_dict["PASSWORD"]:
@@ -269,20 +275,13 @@ class DatabaseWrapper(BaseDatabaseWrapper):
         connection = self.Database.connect(**conn_params)
         if set_isolation_level:
             connection.isolation_level = self.isolation_level
-        if is_psycopg3:
-            connection.cursor_factory = (
-                ServerBindingCursor
-                if options.get("server_side_binding") is True
-                else Cursor
-            )
-        else:
+        if not is_psycopg3:
             # Register dummy loads() to avoid a round trip from psycopg2's
             # decode to json.dumps() to json.loads(), when using a custom
             # decoder in JSONField.
             psycopg2.extras.register_default_jsonb(
                 conn_or_curs=connection, loads=lambda x: x
             )
-            connection.cursor_factory = Cursor
         return connection
 
     def ensure_timezone(self):
diff --git a/docs/releases/4.2.1.txt b/docs/releases/4.2.1.txt
index f8a4edf787..dd172a1a89 100644
--- a/docs/releases/4.2.1.txt
+++ b/docs/releases/4.2.1.txt
@@ -18,3 +18,7 @@ Bugfixes
 
 * Fixed a regression in Django 4.2 that caused aggregation over query that
   uses explicit grouping to group against the wrong columns (:ticket:`34464`).
+
+* Reallowed, following a regression in Django 4.2, setting the
+  ``"cursor_factory"`` option in :setting:`OPTIONS` on PostgreSQL
+  (:ticket:`34466`).
diff --git a/tests/backends/postgresql/tests.py b/tests/backends/postgresql/tests.py
index ab66e7ab0e..5589daa0c2 100644
--- a/tests/backends/postgresql/tests.py
+++ b/tests/backends/postgresql/tests.py
@@ -296,6 +296,24 @@ class Tests(TestCase):
         finally:
             new_connection.close()
 
+    def test_connect_custom_cursor_factory(self):
+        """
+        A custom cursor factory can be configured with DATABASES["options"]
+        ["cursor_factory"].
+        """
+        from django.db.backends.postgresql.base import Cursor
+
+        class MyCursor(Cursor):
+            pass
+
+        new_connection = connection.copy()
+        new_connection.settings_dict["OPTIONS"]["cursor_factory"] = MyCursor
+        try:
+            new_connection.connect()
+            self.assertEqual(new_connection.connection.cursor_factory, MyCursor)
+        finally:
+            new_connection.close()
+
     def test_connect_no_is_usable_checks(self):
         new_connection = connection.copy()
         try: