No it's not through an app which would be awesome but through the new and much improved web browser. I have no idea why Sony didn't mention it but it seems the improved web browser has fixed the dropbox support, a site that in the past caused it to crash every time you tired using it. If you got a dropbox account just go to the website and sign in and all your stuff will be there to download. I tried it last night and it works like a charm. The only problem is that the upload might freeze your browser, but this is only a minor issue that has room to be fixed.
Enjoy your shared uploads.