Scientists have stored audio and text on fragments of DNA and then retrieved them with near-perfect fidelity—a technique that eventually may provide a way to handle the overwhelming data of the digital age.

The scientists encoded in DNA—the recipe of life—an audio clip of Martin Luther King Jr.'s "I Have a Dream" speech, a photograph, a copy of Francis Crick and James Watson's famous "double helix" scientific paper on DNA from 1953 and Shakespeare's 154 sonnets. They later were able to retrieve them with...