The 19-year-old, who moved to Upton Park from Manchester United at the end of January, is reported to have made the comment in response to another Twitter user. The FA wrote to Morrison last week for his observations on the matter and formally charged him on Wednesday.
The FA said in a statement: "West Ham United's Ravel Morrison has admitted a charge under FA rule E3 of using abusive and/or insulting words including a reference to a person's sexual orientation in relation to Twitter comments."
The statement added: "Morrison has requested a non-personal hearing."
The FA will now determine the punishment for the offence without Morrison appearing in person.
Morrison was also involved in various off-field controversies while at Old Trafford.
Manchester United allowed the teenager to leave despite him being rated as one of the finest prospects to come out of the club in recent years.
Source: PA
Source: PA