Final answer:
In The Binding of Isaac: Rebirth, Loki's Horns grants the ability for tears to potentially shoot in all cardinal directions based on the player's luck stat.
Step-by-step explanation:
The item in The Binding of Isaac: Rebirth that grants the ability for tears to potentially shoot in all cardinal directions, triggered by the player's luck stat, is A) Loki's Horns. With +7 Luck, it consistently activates. This item can be unlocked by defeating Lokii for the first time.