Two years ago, Facebook Inc. offered its in-house recruiters an incentive to help diversify its largely white, largely male workforce.

Previously, recruiters were awarded one point for every new hire. Under the new system, they could earn 1.5 points for a so-called “diversity hire”—a black, Hispanic or female engineer—according to people familiar with the matter. More points can lead to a stronger performance review for recruiters and, potentially, a larger bonus, the people said.

When...