George Borjas of Harvard and others have a new paper discussing the titular subject. From the abstract:

The employment rate of black men, and particularly of low-skill black men, fell precipitously from 1960 to 2000. At the same time, the incarceration rate of black men rose markedly. This paper examines the relation between immigration and these trends in black employment and incarceration. Using data drawn from the 1960-2000 U.S. Censuses, we find a strong correlation between immigration, black wages, black employment rates, and black incarceration rates. As immigrants disproportionately increased the supply of workers in a particular skill group, the wage of black workers in that group fell, the employment rate declined, and the incarceration rate rose. Our analysis suggests that a 10-percent immigrant-induced increase in the supply of a particular skill group reduced the black wage by 3.6 percent, lowered the employment rate of black men by 2.4 percentage points, and increased the incarceration rate of blacks by almost a full percentage point.