If the wiper blade has its Z axis pointing up through that connection, you can turn on face snapping in Object Mode and enable Align Rotation to Target and that should allow you to snap it right there. If you need it to be 100% exactly to the center of that face, snap the cursor to the face first and then snap the object to the cursor.
Omar also mentioned custom orientations, like shown here, and if you create one you can use Object -> Transform -> Align to Transform Orientation.
