The 21-year-old all-rounder attended a hearing of the England and Wales Cricket Board's disciplinary panel and admitted taking the drug - he will learn his fate on October 18.
Wagg, who apologised for his misdemeanour, tested positive after a random drugs test following a one game between his county Warwickshire and Gloucestershire.
"Mr Wagg is deeply remorseful and determined to show his employers and cricket fans that he will accept the punishment meted out to him," read a statement issued on his behalf.
Wagg made an immediate impact in the sport when he took five wickets on his Championship debut against Somerset two years ago and toured India with England A last winter.
However a persistent back injury saw him fail to play in any of Warwickshire's county championship matches this season as they went on to win the title.
Any cricketer found to have taken a prohibited substance can expect a lengthy ban from the game.
England international Ed Giddins was suspended for 18 months in 1996 after traces of cocaine showed up in a random drugs test while he was at Sussex, who subsequently sacked him.