This is a Microsoft Word forum, not pdf. That said, it may be possible to import the pdf files into Word, add the border, and then re-save as pdf.
If you already have them as Word files, the opening the pdf in Word stage would not be needed nor desirable.
I have no idea how happy you would be with the results. Do not overwrite your originals with the altered versions.
Here are two utilities for bulk processing Word files.
Both let you add your own process to run. In this case, it would be opening the file in Word, adding the border, and then saving in a different folder with the same name.