No, browsers only allow single-line input for prompt(). However, with a simple change to the jQuery Alert Dialogs library you could get multi-line input there. Take jquery.alerts.js, look for <input type="text" size="30" id="popup_prompt" /> and replace it by <textarea rows="5" cols="30" id="popup_prompt"></textarea>. That should do to have a multi-line input field show up when calling jPrompt().

Edit: As Mulletfingers999 points out in a comment, jQuery Alert Dialogs have been deprecated in favor of jQuery UI dialogs. There you can also show a "modal" dialog, that dialog can have arbitrary content however - meaning that a <textarea> tag is possible if you want multi-line input.