There are 2 possible ways to size the TextBox depending on its Multiline property.
Multiline = false Only the width of the TextBox can be changed in this case (the standard TextBox cannot be sized vertically either in that case). To change the width just drag the right or left border of the control. Here, the height of the text box is determined by the font size. If RadTextBox seems too thin you can set some Padding for the text element. To do so open the ActionList for the text box and click on "Edit UI elements". Then select RadTextBoxElement and set its property Padding (see attached screenshot).
Multiline = true In this mode the height of the text box can be of any value thus allowing different number of rows in it.
Please inform us if your case is different than the described above.