An optical rectenna—a device that directly converts free-propagating electromagnetic waves at optical frequencies to direct current—was first proposed over 40 years ago, yet this concept has not been demonstrated experimentally due to fabrication challenges at the nanoscale^,. Realizing an optical rectenna requires that an antenna be coupled to a diode that operates on the order of 1 PHz (switching speed on the order of 1 fs). Diodes operating at these frequencies are feasible if their capacitance is on the order of a few attofarads^,, but they remain extremely difficult to fabricate and to reliably couple to a nanoscale antenna. Here we demonstrate an optical rectenna by engineering metal–insulator–metal tunnel diodes, with a junction capacitance of ∼2 aF, at the tip of vertically aligned multiwalled carbon nanotubes (∼10 nm in diameter), which act as the antenna^,. Upon irradiation with visible and infrared light, we measure a d.c. open-circuit voltage and a short-circuit current that appear to be due to a rectification process (we account for a very small but quantifiable contribution from thermal effects). In contrast to recent reports of photodetection based on hot electron decay in a plasmonic nanoscale antenna^,, a coherent optical antenna field appears to be rectified directly in our devices, consistent with rectenna theory^,,. Finally, power rectification is observed under simulated solar illumination, and there is no detectable change in diode performance after numerous current–voltage scans between 5 and 77 °C, indicating a potential for robust operation.