From Stars and Stripes:

Capt. Simratpal Singh, 27, was granted the appearance waiver last week that will allow him to grow his beard and hair and wear a turban through at least Jan. 8, Debra S. Wada, the assistant secretary of the Army for manpower and reserve affairs, wrote in a Dec. 9 letter. Singh is the fourth Sikh soldier in recent years to be granted such uniform exemptions.

The current dress code is a result of WWII regulations that are still in effect today. There were no such requirements in the early U.S. military. Just look at all the beards on soldiers during the Civil War.