General Zaroff tells Rainsford that the men are capsized in their ships by an act of God or he helps it along with the push of a button that causes flashing lights.  This is supposed to warn sailors that they are approaching a channel when in reality they are coming upon jagged rocks that will crush their ships.  Sailors take the bait and end up on the island as bait for Zaroff and his hunt.

Zaroff tells Rainsford, "I hunt the scum of the earth-sailors from tramp ships-lascars, blacks, Chinese, whites mongrels-a thoroughbred horse or hound is worth more than a score of them."

I always got the feeling that it was a combination of the two.  He "traps" ships as they come close enough to his island, but he also goes out into the world looking for those who won't be missed by their families.

Zaroff's island is called Ship Trap Island. He shows Rainsford the lights he has in the water to make ships think that there is a safe channel on which to sail. In reality, there are jagged rocks that will break up a ship, causing the crew to seek help once their ship begins to sink. The only place on the island to get help is Zaroff's place.

Zaroff says

"I hunt the scum of the earth sailors from tramp ships—Lascars, blacks, Chinese, whites, mongrels—a thoroughbred horse or hound is worth more than a score of them.''

From this statement, I would infer that he makes periodic trips to the docks of large ports and hires sailors which he then brings back to his island and hunts.  The story was written in the 1920's and Zaroff has many of the poor stereotypes of immigrants common in America at the time.  He would think nothing of enticing these "scum" sailors to his island on false premises for his hunting pleasure.