Go into the Precision menu and turn on Smart Guides. Then tap outside of the mirror repeat object to deselect it, tap on it once to select and move it (see a dotted line around the whole object). You'll see a magenta highlight light up when you drag the mirror repeat object horizontally over the center of the artboard and it will snap to that center. To go back to editing, double-tap the mirror repeat object and you can move the circle where you want it. Also, if you want to align to another line, not in the center, you can create a guide in the Precisions menu > Add guide. Once you've placed a guide where you want it, the smart guides can snap to it.