The Daily Dot investigated this claim and found that the yearbook does in fact credit Ted Cruz as a mime Adam (and as you can see he is also barefoot):
Travis McWilliams, representing God and Ted Cruz as Adam act out the creation in a mime. Photo by M. Neath.
They also interviewed two classmates of Cruz's, Clint Rosenthal and the photographer of the picture "M. Neath":
“I was in 5th grade and didn’t really know [Cruz],” recalled Clint Rosenthal, the tipster who sent the mime photo. “I assume I was in the audience since that appears to have been during Chapel. I guess I suppressed that memory.”
“What I can say,” Rosenthal continued, “is that the biblical version of the creation of man (and ladies from Adam’s rib, etc.)—the subject of Cruz’s interpretive mime performance—was taught pretty literally there, so I’m betting a lot of folks in the audience were thinking he nailed it. Hell, it made the yearbook.”
“M. Neath,” the person who took the photo, would surely know more. I found a smattering of search results for a Mark Neath, about Cruz’s age, and contacted him via email.
“I was a classmate of Ted’s at Second Baptist School and a photographer on the yearbook staff, so I evidently did take the photo,” Neath wrote back. “I cannot confirm that it is Ted, but it certainly looks like him. The photo captions were pretty well-researched, and it was a very small school, so it would be surprising if it is wrong.”
Cruz eventually became president of the drama club, so he was definitely involved in theater.