Yes. There is a feature called AutoFormat.

Do it on a copy. Chances are you will not be very satisfied with the results.
The optional settings can be found under File > Options > Proofing > AutoCorrect Options > AutoFormat (tab)

You would want to add the AutoFormat command to your QAT.
Modifying the Quick Access Toolbar (QAT) in Microsoft Word



Otherwise, see Cleaning Up Pasted Text by Suzanne Barnhill, MVP