Well you could, but I don't think it'll work too well. It's likely that the sour orange tree was once just a rootstock with a different, most likely sweet, orange grafted above it. Since that original graft has obviously died back/disappeared, the rootstock has taken over and grown away in its own right, so your grafting a piece of the sweet orange onto one branch might mean, if the graft takes, that one branch will produce sweet oranges, but the rest of the sour orange will still be present, taking away nutrients from your grafted branch. Once rootstock takes over and grows on its own, it's usually much more vigorous than the grafted parts, so any attempts to graft it now, at what is presumably a large and mature size if it produces that many fruits, will likely be futile.
Try it if you want to though, otherwise, your sour oranges might make very good marmalade.