Gun sellers are using a simple trick to do business on Facebook Inc.’s Marketplace at a time when more mass shootings in the U.S. have renewed the debate in Washington over access to firearms.

The Marketplace feature, which Facebook launched four years ago, enabled its more than two billion users to buy and sell almost any secondhand item by clicking a button on their home page. However, the private sale of many items, including guns, is specifically forbidden under Facebook policy.

To...