I've never heard of this anywhere in the US (but I've never explicitly looked). I got a plot at work once but that was private property. A senior center next to me offered gardening at a nearby plot for it's elderly members but again nothing public. Some city parks have small gardens run by volunteers.

Edit: should have googled, seems my town does indeed have it! https://www.mountainview.gov/depts/cs/rec/facilities/garden....