Spawns a familiar that stabs Isaac at the beginning of each floor, if Isaac has more than half of a red heart. This will drain as many red hearts as possible without killing him (leaving half a red heart if Isaac only had red hearts, or none at all if Isaac has soul/black/bone hearts).
Even though the animation is only a single stab when the effect triggers, it is treated as taking damage one time per half heart lost. This can lead to great synergies with items that activate on damage taken.
For the rest of the floor, Isaac gains +(0.15 * HeartsLost ^ 2) damage and +(0.1 * HeartsLost) speed, where HeartsLost is the total hearts of damage taken from Blood Oath (half a heart counts as 0.5).
This amounts to a max of +19.8 damage and +1.15 speed if starting the floor with 12 filled hearts (of which only 11.5 are drained).
This increases to +21.6 and +1.2 if starting the floor with 12 filled hearts, at least one being a Bone Heart.
Isaac can avoid damage from Blood Oath with invincibility, but he won't gain the damage and speed increase if he does.
Eternal hearts give the health up before Blood Oath stabs Isaac, draining that extra heart too.
It's also possible to use XI - Strength at the beginning of a floor before getting hit by Blood Oath to have one more heart counted in the bonus.
If Isaac has only half a red heart, the effect will not trigger at the start of the floor, even if Isaac has soul/black hearts. Having no red hearts at all also prevents the effect from triggering.
The familiar will appear much bloodier when a large amount of hearts are drained.
PC A088 LA10 (Curse Room adjacent to spawn)
Using Glowing Hour Glass to return to the previous floor twice will cause Blood Oath to activate an extra time, retaining buffs from both activations. If Isaac was at half a heart when the stab happened, it instead will nullify all buffs and deal no damage.