Dropbox has no such feature. You'll need to find a third-party app or service to do that. There are also websites that can merge PDF files for you. One such site, smallpdf.com, has many free PDF utilities.
@Daphne wrote:Just to add to what @Rich mentioned, you can choose to open your PDF on the Dropbox website with a selection of 3rd party apps, including smallpdf!
Ah, nice! I hadn't noticed that in the apps list before. Thank you!
PDFWRENCH.com - it's the free online tool, but it does not upload files, files stay at your computer.