There is no way to do that with current versions of FileMaker using the tools that it comes with. Don't know of any plug ins that can do this, but it's worth doing a web search to see.
In theory, you might be able to copy and paste all the text from a page of your PDF into a text field in your database and then a script might be able to parse out the individual values you need from the PDF, but this would not be a trivial operation.
Alternatives you may want to consider:
If you were to publish to the web, your clients could fill out this form in their web browser and the data would be entered directly into your database.
If you have FileMaker Advanced, you could create a small runtime solution that your clients could install on their computer. They could fill out the form on a FileMaker screen and then the a runtime file could be emailed back to you where a data import can import the data into your database.
You could send a file to people with iOS devices and they could use FM GO to fill out the form without having to create a runtime soluton.