When the RadRotator is set with the Sitefinity built-in skin and it is configured in a mode with buttons, the buttons are not displayed.
You can workaround the problem by adding the following CSS code on the page with the rotator:

<style type="text/css">
    div.RadRotator_Sitefinity .rrButton.rrButtonRight {
        right: 0;
    }
 
    div.RadRotator_Sitefinity .rrButton.rrButtonLeft {
        left: 0;
    }
</style>