Randy Travis Cited in Church FIGHT -- 'Extremely Intoxicated'

2:00 PM PT -- Travis had "bloodshot" eyes and torn clothing following the incident ... this according to the police report.

11:38 AM PT -- A source close to Randy tells TMZ, the singer was NOT drunk, nor had he been drinking. The source says Randy's fiancee and her estranged husband were arguing over visitation of their son and things got violent ... so Randy jumped in.

7:45 AM PT -- The Plano Police Department tells TMZ ... Travis was cited for simple assault. We're told officials believe Randy was the primary aggressor.

Cops say ... there was a "family argument" taking place between a man and a woman ... and Randy got involved.

Randy's lawyer, Larry Friedman, tells TMZ ... the woman in the argument is Randy's fiancee, who was arguing with her estranged husband ... when Randy entered the situation.

Friedman says, "Randy Travis was the only man that came to the rescue ... fortunately even today chivalry is not dead”

Another man was also involved in the fight, but cops say it wasn't the husband.

More trouble for Randy Travis ... TMZ has learned the embattled singer was involved in a FIGHT in a church parking lot in Texas early this morning.

Law enforcement sources tell us ... cops responded to the church around 1 AM after receiving a tip about two men fighting in the parking lot.

We're told Travis was taken to the hospital after the fight. One source tells us Randy appeared to be "extremely intoxicated."

We're told the fight was over a girl.

Travis has had serious problems with alcohol -- he was arrested for DWI earlier this month after cops say they found the singer naked at the scene of a car crash.

And Travis was busted for public intoxication back in February after cops say he was hammered in a different church parking lot.