An 18-year-old native of El Salvador was charged last weekend with breaking into a Brooklyn, N.Y., home and raping an 11-year-old girl. When police apprehended the suspect, a reputed MS-13 gang member, he was carrying a forged green card. Two weeks ago authorities in Iowa charged a Mexican farmhand, also believed to be in the country illegally, with first-degree murder in the death of college student Mollie Tibbetts.

Violent crime in the U.S. has plummeted in recent decades, and studies repeatedly have shown that legal and...