Even if the player does not get a hit in his at bat, a run scored when he puts the ball in play will count as a run batted in. An RBI will still be given on an error provided that the potential put out would not have been the third out of the inning. A run scoring on a double play does not qualify as an RBI, however.
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Yes, the player is credited with a RBI.
RBI stands for "runs batted in", the number of runs the player pushes across the plate with a hit, a walk, etc.
Eddie Murray, 996
Honus Wagner with 1732 RBI
8, by Fernando Tatis, St. Louis Cardinals, April 23, 1999, in the third inning.