On the upper slopes of Mount Targon, the warriors of Rakkor live and breathe only for war. However, Targon’s peak is reserved for a special group of Rakkor who answer to a “higher” calling. Members of this group, called the Solari, retire their mantles of war, choosing instead to devote their lives to reverence of the sun. According to legend, the Solari were formed by a warrior who could call the raw might of the sun down upon his enemies in combat. He claimed Mount Targon’s summit, the point on Valoran closest to the sun, for his solar devotion, a tradition which generations of Solari have preserved to this day. Though they maintain their reverence, no other warrior possessed the gifts of the founder – until Leona.

Leona’s parents were traditional Rakkor, both bred for the heat of battle. To them, Leona was a problem child. She was capable of fighting as fiercely as any other – including her childhood friend, Pantheon – but she did not share their zeal for killing. She believed that the true worth of a soldier lay in her ability to defend and protect. When it came time for her Rite of Kor, a ceremony in which two Rakkor teens battle to the death for the right to bear a relic-weapon, Leona refused to fight. For this, the Rakkor leaders ordered her execution, but when they tried to strike the fatal blow, sunlight burst forth, bathing Mount Targon in light. As it faded, Leona stood unharmed and her executioners lay unconscious around her. The Solari immediately claimed Leona, demanding that her sentence be repealed. She donned the golden armor of the Solari and they bestowed upon her the sword and shield passed down from the ancient sun-warrior of legend. The Solari helped Leona focus her abilities, and when she was ready she left to join the League of Legends.

“The sun's rays reach all of Runeterra, so too must the image of its champion.”
―Leona

I've heard this lots "We got a troll jungler" or "omfg does it actually work? K cool gg" but nothing to fear, her jungling is great as long as a good leash from mid suffices. Her w will help her greatly to jungle as her e will make her so good with ganks that she will terrify that dastardly top lane!

PROS:
Scary Ganking Capabilities
Tanky and Brut-ish
Keeps great cc on jungle and heroes
Great Support

CONS:
Harder if leash isn't given properly
Counter Jungle-able
Not in the kitchen >:P

Lets face it, u want to keep that one target cc TO THE MAX for ur team to take out, so to my standards SMITE EXHAUST are the best for Leona Jungle :P

These are the effects of other summoner spells:
TELEPORT Not so good with junglers, like ive said, good if u have a super warding support that places tactically
FLASH U can replace EXHAUST for this if u feel like their team is very escape like. Ur ulti should be the preventer of escapes, but meh, flash is a good alternative
IGNITE If u really want them kills, then replace EXHAUST, but ur suppost to support tank, so its kinda not ur role. but whatever im not u. I would say its decent with her
HEAL Shes got too much hp to give a **** about healing
GHOST Not really a point due to having good mvtspd and ranged cc. i would say no, unless they got alot of slows
CLARITY um.... yes? jk no...
EXHAUST Very good for keeping that one hero from escaping u and/or ur team. That one carry or fed fck could be the kill ur team needs to Nash rush or even win. Yes for exhaust
CLAIRVOYANCE Only if ur very cautious with her, other than that she does need it at all, shes jungling ffs
REVIVE Only time ill use this is when im eating KFC and die of a heart attack or aneurism.
PROMOTE Promote Dergun???
SMITE Core spell for jungling needs, itll prevent Leona losing so much hp at blue and keep her income up if ganks dont do as well (which they wont cause its BAU5 to gank with her)

The items used for this build are the best, but just in case of other alterations, ur MERCURY TREADS can be replaced with BOOTS OF SWIFTNESS to keep up with enemies. IF u ever want to keep up the health regen, which isnt to much of a problem due to massive amounts of hp, u could replace ur BANSHEE'S VEIL with a FORCE OF NATURE so u can come in and out of team fights or poke and run. thats for ******* though. like MUNDO!!!
U can always replace ZEKE'S HERALD with a BLOODTHIRSTER if u just feel like ur on top of the world :P but id stick with ZEKE'S HERALD to keep ur tank, and supportive side