No, the site doesn't offer that. I seem to recall some discussion erik was involved in where that was asked but don't recall what his take was.
Your best bet is to just put them all on a DB program. Keep a copy online somewhere. I use SCID vs PC and keep my databases synced to Google Drive.
Like most people, I have a bunch of scoresheets scattered around, plus games entered in a couple of different notebooks. I'd like a convenient way to enter and keep all my games in a computer database so that, not only do I have access to them, but can bring them up at any time for further analysis. This would be a lot more convenient than dragging out the pieces, setting them up, playing over the game, trying out some variations, and then forgetting the original position and having to start over.
Does chess.com offer such a feature?