Measuring the cosmic ray flux over timescales comparable to the age of the Solar System, ∼4.5 Gyr, could provide a new window on the history of the Earth, the Solar System, and even our Galaxy. We present a technique to indirectly measure the rate of cosmic rays as a function of time using the imprints of atmospheric neutrinos in "paleo-detectors," natural minerals that record damage tracks from nuclear recoils. Minerals commonly found on Earth are ≲1 Gyr old, providing the ability to look back across cosmic ray history on timescales of the same order as the age of the Solar System. Given a collection of differently aged samples dated with reasonable accuracy, this technique is particularly well-suited to measuring historical changes in the cosmic ray flux at Earth and is broadly applicable in astrophysics and geophysics.