Doug's answer is correct, but in case you are new to all of this, you would create the artwork in another program, which could be Illustratror, then make the PDF, then create the form in Acrobat. What you are asking for would probably require some JavaScript, as Acrobat can't do that straight out of the box.
You probably want to test it before you get too far, and ask for advice on the Acrobat forums:
Acrobat
If you don't know JavaScript, you might be able to hire someone to write the code which you can copy and paste into the field.