Neither J.R.R. Tolkien nor his son Christopher ever produced a detailed map of the lands of Rhûn (nor of Far Harad, for that matter). Nor did Tolkien ever describe those lands in any detail except for the times of the Years of the Trees and The Years of the Sun preceding the First Age.
Tolkien did sketch out rough maps of Arda in those earlier times; those maps have been reproduced in the HOME volume The Shaping of Middle-earth. But those sketches don't give us a good idea of what the East and South of Middle-earth look like in the Third Age, or how the destruction of Beleriand and the sinking of Numenor affected the Empty Lands beyond the coasts of Middle-earth.
Arda in the First Age by J.R.R. Tolkien:
Both Weta and Amazon Prime have released maps that depict the Orocarni (Mountains of the East), though I've wondered if the range should be set a bit farther to the east.
Is there a full canon map of Arda, somewhat detailed?
@ShireofMiddleEarth Not a canonical one, no. However, the late Karen Wynn Fonstad drew maps of Arda based on Tolkien's sketches for her revised Atlas of Middle-earth. I highly recommend the book.