What your describing isn't really a roatation its a translation with a linear fall off to your pivot. You just want to be able to describe this translation with a rotation.

There isn't something which maya will support though you could probably do it with a soft modification though it wouldn't give you a rotation handle.

If you use a soft modification deformer and place a locator at your pivot with a look at constraint toward the soft mod deformer you will be able to get an angle feedback of your translation.