Thank you for posting your request to History Hub.
There are two series which may of be help to you, which I will link here from our catalog.
Consolidated List of Men Subject to the Draft, 1863 - 1863
List of Men Who Were Drafted or Who Furnished Substitutes in the Supplemental Draft Call of July 18, 1864, 8/1864 - 11/1864
In order to search these lists for the record, you would need to try to narrow down more information on the specific gentleman you are searching for. In order to effectively search the consolidated lists, we would need to know the town or city in which he registered. Also, be aware that as an alien, he would not have been required to sign up for the draft.
The actual draft records are held at the regional facility for the area in which he was drafted. If he did indeed register for the draft, you could also reach out to either our Riverside Facility or our San Bruno facility. I have linked both of their websites, which list the regional records they hold.
National Archives at Riverside
National Archives at San Francisco
I hope this is helpful in your research!