In doing so, Arcia became the first player to catch, pitch and homer in the same game in the modern era (since 1900), according to Elias Sports Bureau.
Informed by the Angels of his feat, Arcia said, "I'm pretty happy, I guess."
Arcia, 29, was already in the record books after driving in 10 runs in his first two games after being called up from the minors on July 26.
Arcia also became the first Angels position player to pitch since 1993, when he threw one scoreless frame against the A's on Aug. 11, but hadn't done much since.
That changed Thursday when the Angels fell behind by double digits early. Manager Mike Scioscia felt no need to tax his bullpen, so he turned to Arcia.
"Just BP fastballs," Arcia said when asked what his repertoire included. "Played catch with my catcher, that's it."
Arcia then homered off Chris Hatcher in the ninth.
"That's a nice little note for Frankie, for sure," Scioscia said.
"I just play hard," Arcia said. "Wherever they put me, I'll play hard."
The Associated Press contributed to this report.