How can one wash a woven leather carpet?

how is it woven? Where do you live?

"A quality rug can add taste and texture to a room, warm up floors that are cold to the touch and absorb echoes in a sparse living space. Leather rugs are no different, but they can be a sizable investment in comparison to wool or cotton rugs, so buyers would be wise to take great care of them at all times. With proper cleaning, a leather rug can be a centerpiece for your room and a valuable heirloom." https://www.hunker.com/13419915/how-to-clean-a-leather-rug

Make sure you use quality leather cleaners and conditioners to make sure the leather stays supple and doesn't start to crack. I kept the leather seats in a twenty five year old car supple with no cracks or wear marks using leather cleaner and conditioner on them a couple of times a year, but you may want to do it more often since they will see more abuse than my car seats did.

Some leather rugs can be cleaned with a mixture of mild soap and water but I would check with the manufacturer and see what they recommend.

Use a good leather cleaner. The best can be gotten at a farm supply store. I used to won horses and would never use water to clean my leather saddles!

That's own not won horses! Sure we had an edit button!

I have never seen a leather carpet but I would think it's no different than well used leather furniture...I do leather work and would suggest a leather cleaner and conditioner, don't skimp on the cheapest one...do your research!