Interesting question. The thinking here is that very few were, since the draft only applied to the Union States, and the vast majority of blacks were slaves in the Confederacy when the war bagan. But there were a significant number of blacks who volunteered for service in the Union army after they had been freed, and who joined segregated black units.
No. Blacks were not drafted by the Union in the Civil War. They did form some volunteer units.
There was virtually no draft for blacks, but 198,000 volunteered for and were accepted into the Union army and navy between 1862 and 1865, by the latter year comprised about one tenth of the entire Union armed forces. Many others were pressed into labor and other support jobs for the Union army, or volunteered as spies behind Confederate lines or as laborers when Union armies were nearby.
http://www.archives.gov/education/lessons/blacks-civil-war/