It seems to be a tradition that U.S. Presidents have their genealogy traced for them, even without asking. There is an old joke that seems to be true: "To get your family tree done the fastest, run for political office."
Indeed, there is truth in that old joke. In fact, Joseph R. Biden, Jr. has already had his ancestry researched by a number of researchers and it has been published on several web sites.
By the way, did you know Joe Biden's middle name is Robinette? He inherited that name from his great-grandfather, George Hamilton Robinette (1844-1914), a Civil War veteran. It was also the middle name of the new President's father.
Listings of Joe Biden's ancestry are available all over the Internet. Two different sites caught my eye:
Family of Joe Biden on Wikipedia at https://en.wikipedia.org/wiki/Family_of_Joe_Biden provides a brief, but easy-to-read listing
Ancestry of Joe Biden by Rich Hall at https://famouskin.com/pedigree.php?name=48077+joe+biden&ahnum=1 provides a more detailed listing going back 10 generations in one line that will probably appeal to experienced genealogists.
My preference is the ahnentafel (list of ancestors) from Rich Hall's listing:
Look → Click or tap a name to see more details including sources or famous kin.