do you have to pay rune to equip items to your tokens?

Yes — tokens are units, so equipping to them works exactly as normal and you pay the full Equip cost.

Equip is an activated ability short for "[Cost]: Attach this gear to a unit you control" (Rule 818.1.c.2), and a token unit is a unit for all effects and actions that choose units (Rule 185.2.d; FAQ 9299 confirms attaching gear to a Sprite token). There is no free-equip rule for tokens: you pay whatever the Equip cost says — energy, power (recycling the rune for a domain symbol), or any non-resource cost listed (Rule 818.1.c.3).

The only discount path is a card-granted one, e.g. Emperor of the Sands gives your Sand Soldier tokens Weaponmaster, which reduces the Equip cost by [A] — still a payment, just smaller. Note that an already-attached gear can't be re-equipped without Weaponmaster, since its rules text goes inactive (Rule 718.2).