The only WWII Draft Registration Cards released by the NARA is the "Old Men's" or the fourth of 1942. Those men bornborn on or between 4/27/1877 and 2/16/1897 - men who were (between 45 and 64 years old) and who were not already serving.
The younger men can still be living today (my husband is) and I do not see any release for online access for just anybody for a few more years.
But from the NARA website..."To obtain a copy of a WWII though Vietnam era (men born April 28, 1877 to March 28, 1957), Selective Service Record, please mail a Selective Service Request Form to:
National Archives & Records Administration ATTN: Archival Programs P.O. Box 38757 St. Louis, MO 63138"