Can I upload a document for the applicant to fill out?

Yes, you can allow the users to download the file, fill it on their end and then upload it to your form. 

This guide will help you allowing your users to download a file: https://www.jotform.com/help/431-How-to-Add-a-Downloadable-File-to-Your-Form 

This guide will help you allowing your users to upload the file to your form: https://www.jotform.com/help/332-How-to-Create-File-Upload-Forms 

I hope this helps.