The logic behind the RadToolTip control is to resize itself according to its content. That is why for the time being we are not planning to implement methods which allow setting the size on the client.
What I can suggest is the following:
Set the size of the content and the RadToolTip will wrap it and take the desired size.
Reference the RadToolTip's popup element and resize it by using its style attribute.
For your convenience I am attaching a sample project which demonstrates my second suggestion.