Sure. It was tried once, initiated by the House in 1805 before the Senate killed it. All you need is a serious violation of law or ethic. You can also raise an amendment to the Constitution, but both are arduous tasks and this one is a fool's errand.Chief Justice Roy Moore Says Supreme Court Justices Can be Impeached http://www.christiannewswire.com/news/3787476347.html
Maybe Moore should helm the try.