According to a poll of 1,935 registered voters released by research firm Morning Consult, about 39 percent of respondents view Cook favorably. The poll was conducted earlier this week and has a margin of error of plus or minus 2 percent.
Cook's approval rating is second to Zuckerberg's, which was 48 percent.
The poll comes as Apple has been embroiled in a high-profile legal dispute with the FBI, who wants the tech company to help access encrypted data on an iPhone used by one of the San Bernardino, California, shooters. Citing privacy and trust reasons, Cook has rebuffed the law enforcement agency's requests.
Morning Consult found that about half of registered votes believe that Apple should comply with the FBI's request to unlock the iPhone. Those findings echo the results of a recent Pew study, which also found more support for the agency's position than for Apple's.