While this tutorial shows how to round the corners of a colored square, you can use this technique to round the corners of any rectangular frame.
With the Rectangle frame Tool selected, Shift + drag to draw a square frame. Click a swatch in the Swatches panel to fill the frame with color. Type V to switch to the Selection Tool.
Click the yellow handle that appears on the right side of the frame.
Yellow diamonds appear at each of the four corners.
Click and drag one of the diamonds toward the center of the frame to round all four corners equally.
Tip: Click outside the selected frame to stop editing corners.
With the rectangular or square frame selected, click the yellow handle to view four yellow diamonds at the frame’s corners.
Tip: To remove a rounded corner, type Command + Z (Mac) or Control + Z (Win) to undo.
To remove all the rounded corners on a selected frame, choose Object > Corner Options. Choose None in the flyout menu for any corner, and click the Make all settings the same icon.