Currently that is not possible (or atleast not easy to do). But I've added a new property that will allow you to accomplish this. This will be available in the next maintenance release.
What is this property called? I see HorizontalContentAlignment, but that is obviously inherited from the System.Windows.Controls.Control and doesn't seem to have any effect on the text value's alignment. I'm using version 9.2.513.0.
The property is called PartEditBox.CenterSlotHorizontalAlignment. The PartEditBox hosts items in one of three slots: left, center, or right. This alignment only affects the items in the center slot, which is typically considered the "real" content.
Our Sample Browser has a QuickStart that shows this option off also.