Take it to a self service car wash. Spray the heck out of it and let it dry in the sun.

It's probably too late for this (and you might be in the wrong climate altogether), but snow cleaning works great. You want fresh snow that is powdery, and at least a few inches of it. You bring your rug to the outdoor temperature (on a porch or in the basement), and then lay it facedown on the snow and stomp on the backside. Peel it up (you'll see lots of dirt on the snow below) and try again in a different spot. Then brush it off and bring inside.

There are solvent-free drycleaners out there:

http://www.greenearthcleaning.com/

When I was a kid, living on a farm, it was my job to clean the braided rugs.

Step 1: hang the rug on a clothes line or off a tree and beat the rug with a paddle
(if the rug isn't too dirty, you can get away with only doing this step)
Step 2: rinse the rug with the hose, and use dish detergent and your hand to scrub out stains.
Step 3: rinse out all the soap
Step 4: Let it dry

Do you have power washer? This is how I clean all of my rugs even the 50 some odd year old Persian ones. I take them outside wet them with the power washer and then pour on some laundry detergent, use a semi stiff bristle brush attached to a broom handle and scrub away at the surface until it's nice and soapy, let it sit for a bit and then rinse with the power washer. Sometimes I skip the soap step it depends on how dirty the are. A great way to speed the dry time is to use a board like a two by four get down on your hands and knees and push the water out of the rug using it like a squeegie. Not sure how well that will work on a braided rug. I have a tied rag rug and I basically just have to wait for it to drip/air dry. I hang mine over my deck rails. Beating them before hand is a good tip. I'm lazy so I skip that step, but I regularly shake my rugs and vacuum both sides so I feel it's enough.

It looks really good just hang it out in the fresh air and let it air it's self out. Shake it a little. Do not wet it, it might get stinky. Even if you dry clean it you can air it out before using it again, it will be ok.

Alternatively, it looks like you could fit that one into a large washer at the laundromat.

Put in a baggie and freeze it ; )

A really knowledgeable kilim dealer told me that I could clean my rugs by putting them in the bathtub with shampoo (I plan to use the wool wash I have for my knitted garments instead) and letting them soak a bit, then letting them hang dry.

I haven't tried it yet, but I'm going to, now that its warm enough they might actually out on my deck.

Eva, too funny

Last summer, i washed my small kitchen rug on my deck outside. I washed it with oxyclean stuff and sprayed it with water. OMG,i didn't realize how dirty the rug was...the water color was brown..pure brown. I am going to do it again this summer.

Danica123 that's what I was going to suggest. Putting it into a large washer at the laundromat. I have this rug and that's what I'm going to do when it need to be washed.

http://www.ikea.com/us/en/catalog/products/40070091

I use Wool Mix with eucalyptus I put my rugs on the sloping drive way scrub with a broom then rinse with a hose ( only if my don't have water restrictions ) I then leave them over my ballistrade to dry

If it is wool don't put it in a big washing machine. Washing is probably fine by the hose/broom/soap method. The tumbling and rubbing action in a washing machine can create interesting felted art object in wools.
Sometimes the dry clean instruction is because the dyes might fade or bleed.