This is yet another of those pesky fungus diseases, similar to Blackspot and Rust. The causes and treatments are also similar.
Just like Blackspot, prevention is better than cure. The spores are often present in cooler damper climates, and will be easily spread by splashing water. So try not to water the foliage. or if you do, then try to do it in the morning so the heat of the day will dry the leaves before the sun goes down. Pick off and discard (not compost) the infected leaves. Rake up any fallen leaves, to reduce the risk of re-infecting the rose next time you water it.
Again, treat this just as you would blackspot. In fact, the blackspot milk treatment should work equally well with Anthracnose. If not, then your garden center has plenty of fungicides that you can use. However, these are not cures, they are more a control measure. That means you still want to be vigilant and pick off any leaves that seem to be infected and discard them.
While Anthracnose is similar to blackspot, I think of it as being more like the “big bad brother”. While blackspot looks ugly, the blooms are not generally affected. However, anthracnose can and does affect bloom quality, so try to keep on top of it. This disease can be a major problem in some areas, not only with roses, but fruit trees and ornamental shrubs.