Perhaps you can paste it into an image editor app and then save it as a file?
Pretty sure the media picker can only pick files on Android.
Also if the image was on screen at some point before it was on the clipboard, you could take a screenshot as a rough workaround. Those are also saved as files.
I actually took a quick look at the Android API to see if there was an obvious way to make an app to do this, and as far as I could find, there is not. It might be impossible.
I'm not aware of any such app and I don't see one that does this with a quick Google search. Is there a reason you're not just sharing the image directly?