This issue is related to a specific browser bug. In this case Internet Explorer does not allow changing the text alignment with JS. However, to workaround it please use the following CSS rule:

html .RadInput .riTextBox {
    text-align: right;
}

For the specific state on the control you can add the corresponding CSS class (riEnabled / riFocused / riHover) on the same selector

html .RadInput .riTextBox.riEnabled {
    text-align: right;
}