Not a comprehensive review, just a summary of the first few studies I found.
A study of adolescents in Minnesota finds finds 2.1% of white males and 7.6% black males report having "used anabolic steroids to gain muscle in the past 12 months" . Other numbers from this study: Hispanic 6.1%; Hmong 14.8%; other Asian 7.9%.
A study of high school football players in Indiana finds "minorities are twice as likely to use AAS" compared to whites .
An NCAA survey finds black college athletes are less likely to report using steroids than white athletes (unfortunately, results by sex and sport further broken down by race are not shown) . Blacks also report less use of every other drug in this study. Considering that other evidence indicates blacks tend to underreport and whites tend to overreport drug use in surveys , I don't find these results terribly convincing.
 Irving et al. Steroid Use Among Adolescents: Findings From Project EAT. Journal of Adolescent Health 2002;30:243–252
 Stilger, GS and CE Yesalis. Anabolic-Androgenic Steroid Use Among High School Football Players. Journal of Community Health, Vol. 24, No. 2, April 1999
 NCAA Research Staff. NCAA Study of Substance Use and Abuse Habits of College Student-Athletes. September 1997.
 Bauman KE, Ennett SE. Tobacco use by black and white adolescents: the validity of self-reports. Am J Public Health. 1994 Mar;84(3):394-8.
Studies consistently show that Black adolescents are less likely than White adolescents to use drugs. [. . .] Only one study has empirically addressed the possibility that Black adolescents might underreport their drug use more than White adolescents. Mensch and Kandel11 found that among youths who had reported in 1980 that they had used drugs, more Blacks than Whites reported in 1984 that they had never used drugs. The one study of young adults that compared Blacks and Whites concluded that Blacks underreported smoking more than Whites. [. . .] Future studies of Black-White differences in drug use that rely on self-reports should account for invalid measurement before proceeding to examine variables of more theoretical and practical interest, or they should give more credence to the possibility that the differences they attempt to explain may be due in large part to differential validity.