The 20-year-old, along with Walsall's Manny Smith have been found guilty of bringing the game into disrepute following their posts on the social networking website
The 20-year-old was also warned over his future conduct after being charged along with Manchester United striker Federico Macheda on Monday.
The pair were accused of acting in a way which was 'improper and/or brought the game into disrepute' which included 'a reference to a person's or persons' sexual orientation'.
Walsall's Manny Smith was also charged by the FA for a similar incident and was fined £1,200 but no details of Macheda's case were confirmed.
An FA statement said: "Newcastle United's Nile Ranger and Walsall's Manny Smith have been fined £6,000 and £1,200 respectively and both warned as to their future conduct after each admitting a charge of using abusive and/or insulting words including a reference to a person's sexual orientation.
"The charges relate to Twitter comments and both players requested a paper hearing."
Former Manchester United midfielder Ravel Morrision was fined £7,000 last week by the FA after making a homophobic comment on Twitter.
The 19-year-old, who moved to West Ham in January, replied to another Twitter user in an offensive manner and was subsequently charged and warned about his future conduct.