A New York City former construction foreman was charged with making workers on a public project cash their paychecks and turn over a portion of their wages to him as kickbacks.

A complaint unsealed Feb. 8 in the U.S. District Court for the Southern District of New York charged Erron Strachan of Brooklyn, N.Y., with violating the Copeland Act, an anti-kickback statute added to the Davis-Bacon prevailing wage law in 1934.

The case is unusual in federal prevailing wage enforcement,...