Can you activate a planeswalker loyalty ability the turn it enters the battlefield?

Planeswalkers can have their loyalty abilities activated on the same turn they enter the battlefield. The 'summoning sickness' rule (CR 302.6) only restricts creatures from attacking or using activated abilities with the tap or untap symbol. Planeswalkers are not creatures (unless a card specifically says so), and loyalty abilities do not use the tap symbol.

CR 606.3 states that a player may activate a loyalty ability of a permanent they control any time they have priority during their own main phase, as long as the stack is empty — with no requirement that the permanent have been under their control since the beginning of their turn.

The one key restriction is that each loyalty ability can only be activated once per turn (CR 606.3), and you can only activate loyalty abilities of planeswalkers you control during your own main phase when the stack is empty.

Example: You cast Chandra, Torch of Defiance on turn 4. She resolves and enters the battlefield. You can immediately activate her +1 loyalty ability during that same main phase — no waiting required.

Note: If a planeswalker also happens to be a creature (e.g., due to a type-granting effect), summoning sickness would apply to its creature characteristics, but loyalty abilities would still be usable the turn it enters, since they don't use the tap symbol.