Cleric with Luck domain. Cant do it till 6th level and a additional time every 6.
Can also give reroll ability to another party memeber 3+wisdom mod. per day.
Dual-Cursed Oracle. Misfortune ability. I'm pretty sure that's allowable for Society play. Maybe. There are also quite a few items that do it. Might be worth looking into, if you're really interested? I think there's also a halfling feat that does it.
15th level Gunslinger (Slinger's Luck) for ST/skill.
11th level Samurai (Honable Stand) for ST.
Level 1 bard spell Saving Finale for ST.
Witch with Fortune hex for anything.
Lessons of Chaldira trait to reroll a save 1/day.
Tandem Trip feat to roll 2d20, take the higher, on trip checks if an ally w/ the feat is also threatening the foe (or any ally threatening if you have Solo Tactics).
Tactics (War) Domain's "Seize the Initiative" to let an ally roll 2d20 for Initiative, take the higher.
Oracle (Time and Battle mysteries) revelation to roll 2d20 and later 3d20, take highest, for initiative.
Divine Interference feat to blow a 1st level or higher spell to make enemy w/in 30 ft reroll an attack it just made and take lower result.
Ooh, isn't there also a level 1 Torag spell that lets you reroll?
Ooh, isn't there also a level 1 Torag spell that lets you reroll?
Yes: Fallback Strategy.
Oracles also have the Borrow Fortune spell as an option, although you're screwed on your next two rolls.