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 presume that you would like to create your own widget that you can add to your jotforms, but I am not sure if you are actually looking on how to add some existing widget to your jotform instead.
If you are looking to create a widget on your own, then yes, that would be possible.
The widget is not created on the form directly, but instead you need to code it and have a server where you will post the widget code to.
Once you have that, you can access your developer version of your account and add the widget, by filling out a simple form and including all the relevant details.
To do that, you should take a look at the following page: JotForm API Widgets
It will explain what you can do and how to do it and it is quite easy to follow. In case you have any questions in regards to creating your widgets, you can do that by going to here: JotForm Developers Forum.
Now if you were just looking on how to add a widget to your jotform, you can do that by following the steps here: How to Add a Widget to your Form
Do let us know if there is anything else that we can assist you with and we would be happy to do so.