So to start with, it's worth pointing out that you can cast Warding Bond on yourself. Touch range spells are described as:
Some spells can target only a creature (including you) that you touch.
Further, under the Targeting Yourself section, it says:
If a spell targets a creature of your choice, you can choose yourself, unless the creature must be hostile or specifically a creature other than you.
You can cast touch spells on yourself unless they specifically say you can't, and Warding Bond doesn't specify that. This is actually not a bad idea - you'll get the +1 to AC and saving throws, and the double damage you'll take will be canceled out by the resistance to damage.
Find Familiar says that:
when you cast a spell with a range of touch, your familiar can deliver the spell as if it had cast the spell.
Your familiar can deliver the spell as if it had cast the spell. This is the only way in which the familiar acts as the caster of the spell. It can certainly deliver Warding Bond for you, but you will still be the caster of the spell, and the "you" in Warding Bond will still be you, not your familiar. This is effectively equivalent to casting it on yourself directly, except that it took your familiar's reaction.
Departing from my previous answer from the rules perspective, Jeremy Crawford has answered this question in a tweet:
Airatome118 @Airatome
@JeremyECrawford Can Warding Bond have multiple active casts if mats are fulfilled? 3 SETS of rings divided out = 3 ongoing separate spells?
Jeremy Crawford @JeremyECrawford
You can maintain warding bond on multiple creatures at once if you have a pair of the rings for each casting. #DnD
Best Answer
Note: This answer was originally based on a tweet by Jeremy Crawford, who used to be considered an authorized source for DnD 5e rule clarifications over Twitter. This is no longer the case. Official rulings are only those listed in the Sage Advice Compendium, and other tweets by Crawford are simply advice. The old answer shouldn't be of much interest but you can find it in this post's edit history.
The rest of this answer, save for the heading, is written by KorvinStarmast, who graciously gave me the permission to copy his answer over mine so the highest voted answer is proper. Now, without further ado:
Warding bond cannot be used on oneself
BLUF: Requiring two creatures (a caster and a target) is implied in the components element of the spell description, and is made explicit by the use of the plural "either of the connected creatures" later in the spell description.
The italicized text implies two creatures - a caster and a target - each wearing a platinum ring, but it does not state that explicitly in this part of the spell description.
"A willing creature" isn't necessarily only "another willing creature," so one could argue that the caster is "a willing creature" who can touch his/her self. That said, the second half of the sentence implies two parties being involved: the caster and a target. The spell
"You create a mystic connection with yourself"
is not the same statement as
"you create a mystic connection between you and {any other different creature than you.}"
The "general rule" arguments about spell targets, self spells, and touch spells seems to have raised its head again. (See a previous discussion on Paladin Smite spells).
Two parties being involved is the common sense / common usage / plain English reading of this spell description.
We see a second and a third person usage, implying the presence of another creature other than the caster.
"You take damage" and "it takes damage": second person and third person references. Two different persons, to different creatures are damaged.
The caster reaching a zero-hit-point condition ending a spell is common result. That is neither a pro nor con element for this question. Outside of edge case magical effects from other spells, their own 'specific over general' you can't be separated from yourself. This description no sense other than for the case of two separate creatures being involved.
Creatures, plural. Two creatures, a caster and a target who needs to be touched while wearing the appropriate platinum ring.
What was implied in previous language is specified at the end of the spell description. "Either" obviously refers to more than one party/creature.
Conclusion:
By reading the specifics of the spell description, the spell requires two creatures, each wearing the appropriate platinum ring, one touching the other, and both staying within 60' of each other for up to an hour for the spell to provide the damage reduction to recipient of this spell, as well as the AC and Saving throw bonuses.
No, you can't cast this spell on yourself because it requires two creatures, each wearing that platinum ring, to create the spell effect.