How to get rounded corners on text boxes in Apple Pages?

Insert a Text box, and while it is selected, click one of the Shape Styles colors (e.g. blue) in the Style panel. With that now blue Text box selected, choose Style > Border > Picture Frame:

and by choosing the selected frame, you now have a rounded corner Text box with a blue fill. The rounded corner effect only works on a Text box filled with color and not on a default transparent Text box. You can change the fill color of that blue Text box to any color from the Style > Fill > Color Fill > Color Chooser globe.

This also works if you choose a rectangular shape, initially change its color from black to blue, and apply the same picture frame border as above. You can double-click within that shape to enter text and the location of that text with the top, middle, or bottom controls under the Text Color selector on the Text panel.