Yes, something can be both a hormone and an enzyme. There are a group of hormones known as peptide hormones. These are proteins (such as enzymes) that act as hormones indirectly (and maybe directly too?). A hormone is a chemical secreted by a cell that has some effect on another cell elsewhere in the body. In this case, the chemical just happens to be an enzyme. You can read about them on Wikipedia
Renin is secreted by the kidney, but its involved in arterial vasoconstriction (outside of kidney cells), so it is a hormone. And its also a peptide/enzyme, so it is considered both a hormone and an enzyme