Does assigning zero damage to a blocker with deathtouch kill that blocker?

Deathtouch states that any amount of damage dealt by a source with deathtouch is enough to destroy the damaged creature (CR 702.2b). The critical word is dealt — zero is not "any amount" of damage in a meaningful sense; it is no damage at all.

During the combat damage assignment step, an attacking creature with deathtouch still has a minimum assignment obligation: it must assign at least 1 damage to each blocking creature before it can assign excess damage elsewhere (CR 510.1c, the deathtouch exception to the "lethal damage" threshold). However, if the attacker simply has 0 power (or is somehow forced to assign 0), no damage is actually dealt to the blocker, so deathtouch never triggers its destruction effect.

CR 119.3 also clarifies: a creature with 0 damage marked on it has not been dealt any damage, and deathtouch only applies when damage is actually dealt. Zero damage dealt equals no damage dealt for all game purposes.

Concrete example: A 1/1 creature with deathtouch is blocked by a 4/4. The 1/1 must assign its 1 damage to the 4/4, which is lethal thanks to deathtouch. Now imagine a 0/1 with deathtouch is blocked by that same 4/4. The 0/1 assigns 0 damage — no damage is dealt — and the 4/4 survives completely unharmed.

Bottom line: deathtouch only kills a creature if damage is actually dealt to it. Zero damage assigned and dealt does nothing, regardless of the deathtouch ability.