His feat included a grand slam in the fifth inning. He completed the cycle with a drive over the head of center fielder Eric Patterson for a triple in the eighth.
The slow-footed Molina lumbered into third, and, after a few pitches to Chris Davis, left with tightness in his right quadriceps and was replaced by pinch-runner Joaquin Arias with Texas leading 7-4.
Molina, obtained from San Francisco on July 1, singled in the second and doubled in the fourth. He became the first major league catcher to hit for the cycle since Chad Moeller did it for Milwaukee on April 27, 2004, against Cincinnati.
Molina is the fifth player in Rangers history to hit for the cycle, and first since Ian Kinsler on April 15, 2009. The triple was Molina's first since April 29, 2009, and his sixth in 13 years in the big leagues.
The last visitor to hit for the cycle at Fenway Park was Andre Thornton of Cleveland on April 2, 1978.