There are a few things that you can try that do a fairly good job of cleaning rust from concrete. The first thing that you need to consider is how long these rust stains have been on the concrete. The longer they have been on the surface, the harder they will be to remove. If the concrete has been stained for a long time, your results may not be as good as you would like. Concrete is a very porous material, and stains, even those that have been on it for a short time, work their way down into the rough surface.
On construction sites, muriatic acid is one of the most commonly used chemicals for cleaning rust and other stains from masonry work. Muriatic acid is a mild hydrochloric acid, so you need to wear protective clothing, gloves, goggles and an old, long-sleeve shirt.
Use a stiff-bristle brush and some elbow grease with the muriatic acid. The idea is to dissolve the stain and put it in suspension in the cleaning solution. Then the cleaning agent needs to be rinsed off completely carrying the dirt, rust or whatever with it.
There are some specific concrete-cleaning products available. These products can be purchased at most hardware stores and home centers. I don’t recommend any specific concrete-cleaning product. There are some good ones on the market, but they are similar to some of the more common household products you may already have around the house. In addition to this, I have had good luck cleaning stains with the more readily available things.
Common household bleach is another readily available cleaning agent that works on a variety of outdoor cleaning jobs including concrete. Jomax is a product that can be used in conjunction with bleach to make it work better. This stuff works like a catalyst to activate the bleach. Here again, you need to use some physical energy pushing a stiff-bristle brush back and forth over the area.
Few detergents by themselves do a very good job on rust, although they do work on other stains on concrete. I believe that if you try some of the recommendations above you’ll have reasonable results.