To imprecate is to deliver a curse or verbally attack someone. You might imprecate a curse against a rival sports team, or even against a sibling.
The verb imprecate is an old-fashioned way to say "curse," meaning either to wish harm or evil on someone, or simply to swear at them. If you're mad enough to say, "Curse you!" or "May your bed be full of fleas!" when your brother annoys you, you imprecate him. The Latin root is imprecationem, "an invoking of evil," from imprecari, "invoke or call down upon."