JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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I am not sure if I have understood your question correctly.
Do you mean to say that you have created a form in JotForm and embedded it in your website. You want to embed the same form in your new website?
Yes it is possible to achieve your requirement. You can embed the same form in any number of website you want. You need to just grab your form's desired embed code and add it in your new website. The following guide should help you how to grab your form's embed code: http://www.jotform.com/help/34-Adding-a-Form-to-a-Web-Page
Hope this helps.
Do get back to us if you meant to ask something else.