It is a verb meaning "have an effect on", so it has to be the verb "affect".
It occurs without "the" or "an" or "no" (or other determiners), so that's another clue that it's probably not the noun "effect", meaning something like "result".
That drug can have
a very powerful ________ (affect=have an effect on?, effect?) on the nervous system.
Nothing you say can _________ (affect=have an effect on?, effect?) my decision.
That joke did not have
the intended ________ . (affect=have an effect on?, effect?)
The stroke he had years ago still continues to _________ (affect=have an effect on?, effect?) his speech.
(Answers: effect, affect, effect, affect)
You've heard of "causes" and "effects"? Well, strangely enough "effect" is almost never a verb unless it means "cause"! And that happens very rarely.