In order to answer this question well, we need to define what it means to be civilized. If we define being civilized as enjoying and discerning the "finer" things in life, then Zaroff is undoubtedly civilized. If we define being civilized as being humane, then Zaroff is far from civilized.
As the story unfolds, we gain knowledge about Zaroff. For example, we learn that he can read English, French, and Russian. Therefore, he is a polyglot, a sign of being civilized. We also learn that he has a refined palate, as he serves Rainsford a delicious meal. Finally, the way he presents himself is also impeccable, a true man of the world. Rainsford even admits this.
They were eating borsch, the rich, red soup with whipped cream so dear to Russian palates. Half apologetically General Zaroff said, "We do our best to preserve the amenities of civilization here. Please forgive any lapses. We are well off the beaten track, you know. Do you think the champagne has suffered from its long ocean trip?"
"Not in the least," declared Rainsford. He was finding the general a most thoughtful and affable host, a true cosmopolite.
From this perspective, we can say that the general was civilized and cultured. However, if we look at what he has created, we can say that he is a monster of a man whose sense of adventure is perverse. That he would hunt people shows that he is not civilized at all.
In conclusion, I would say that Zaroff is not civilized. He is a menace to society and should be in prison.