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You can upload your fillable PDF form to JotForm so that you can easily collect submissions/responses and saved it directly in your JotForm account.
However, if your PDF form is NOT fillable, I am not sure if it will convert it to a fillable PDF form once you upload it in our end. Please note that uploading PDF forms in our end will not make it editable. Which means you cannot edit or change anything on it using our form builder.
Here's the link that you can use to upload your PDF forms: http://www.jotform.com/adobe-formscentral-alternative/. Click the "Import Forms" button and choose the 3rd option.
After successfully importing it to your account, you can see it like this (see screenshot below), you need to redownload the PDF file so that you can automatically collect submissions/responses in your JotForm account.
If your PDF form is not a fillable PDF, I strongly suggest that you recreate the form using our form builder, that will allow you to maximize the user of our features and services. From there, the online form can also be converted to a fillable PDF. Here's a guide about it: http://www.jotform.com/help/312-Fillable-PDF-Everything-you-need-to-know-about-JotForm-Fillable-PDF-Creator
Let us know if that works.