Moore has yet to play a down in the NFL. He was with the practice squads of San Diego and Denver last season. He later signed with the Chiefs, was cut and picked up by the Redskins.
Moore, who was not drafted out of Texas in 2013, is eligible for offseason activities and can play in preseason games before starting his suspension.
The NFL has levied 10 drug-related suspensions against Redskins players since 2011. Defensive players Rob Jackson and Jarvis Jenkins sat out four games last season, and tight end Fred Davis - now a free agent - is suspended indefinitely.
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