Is Rice's Theorem equivalent to the Halting problem?

Question

As I understand it Rice's Theorem seems to imply the existence of the Halting problem. That is, with Rice's Theorem, we can prove that the Halting problem is undecidable. However, to me, it seems like one could write a proof using that the Halting problem is undecidable to show Rice's Theorem. I'm not exactly sure how one would go about proving such a thing (though it seems by contradiction would be the natural thing to do), but it feels to me that that it should be possible?