Can you activate an ability that requires tapping a creature with summoning sickness if the ability doesn't have a tap symbol?

Summoning sickness (formally called the 'summoning sickness' rule) is defined in CR 302.6: a creature cannot attack, and its activated abilities with the tap symbol ({T}) or untap symbol ({Q}) in the cost cannot be used, unless the creature has been under its controller's control since the beginning of that player's most recent turn (or has haste).

The restriction is narrowly limited to those two specific symbols. If an activated ability's cost does not include {T} or {Q}, summoning sickness places no restriction on activating it, regardless of whether the ability is on a creature that just entered the battlefield.

CR 302.6 explicitly states: 'A creature's activated ability with the tap symbol or the untap symbol in its activation cost can't be activated unless the creature has been under its controller's control since the start of their most recent turn.' Abilities lacking those symbols are simply not addressed by this rule.

Concrete example: You cast Prodigal Pyromancer (which has the ability '{T}: Prodigal Pyromancer deals 1 damage to any target') on your main phase. You cannot activate that ability this turn because it uses {T}. However, if a creature instead had an ability like '{2}: It gets +1/+1 until end of turn,' you could activate that ability the same turn the creature entered the battlefield, because no {T} or {Q} is in the cost.

So the answer depends only on whether {T} or {Q} appears in the cost—not on the creature being a creature or having summoning sickness in any broader sense.