Is there a way to require a signature before they can submit a form?

Yes, you can use the E-signature widget, and make it required: https://widgets.jotform.com/widget/signature

If you need to add it to an existing form, please follow this guide: https://www.jotform.com/help/252-How-to-Add-a-Widget-to-Your-Form

Let us know if you need more help, we will be glad to assist you.