This is not done automatically but it's not difficult to do either:
1/Open your image in Photoshop
2/Press Ctrl+A to select all
3/Press Ctrl+C to copy to the clipboard
4/Press Ctrl+D to deselect.
5/Image>RotateCanvas>Horizontally
6/Image>Canvas Size>Double the width and click on the left or right arrow to make the canvas larger on the side you want the symmetry.
7/Press Ctrl+V to paste your clipboard
8/ Press V for the move tool and nudge with the arrows of your keyboard, evt with Ctrl.
9/ Flatten image.
It sounds more complicated that it is, really, and if you did it once and understand how it works, it is really quite easy.
Corel Photopaint has a tool for this.