Well, that will do it. What do you want to do with the answer?
I suggest you put the results of prompt() into a (js) variable and then pass it to the server through an Ajax.Request. You can use the Rails remote_function() helper to write the js for that. Use the :with option to pass the js variable.
Here's an example from an app of mine:
<%= javascript_tag %Q{ function x_add_task() { var name = prompt('Name for new task', ''); if (name == null) return; #{remote_function :url => {:action => 'x_add_task', :id => @obj.id}, :with => "'name=' + name" } } } %>
Then later:
<%= link_to_function 'Add Task', 'x_add_task()' %>