if it no need to snap to precise center of face, then I have a 1 click solution for this with option to duplicate or just rotate to the face
Since CAD addon is free I think there is no conflict with posting here another one free addon? If so, then I just remove this message.
Summary
keKit for Blender (2.8+)
and its feature Unrotator (checkbox Center on Face and Rotation Offset didn’t work right now)
Also if its one mesh object, then you can use Loopanar addon to place face to face separated meshes
https://www.youtube.com/watch?v=O7ZmqPnfIMU