Rose plants are apt to fall victim to a variety of diseases. Symptoms that include orange spots are indicative of a fungus. Diseases are largely controlled through cultural measures.
Orange spots on rose leaves are typically the result of rose rust. The disease is the result of a fungus, Phragimidium mucronatum, which often targets older leaves first and then spreads to younger leaves.
Rose rust causes orange, brown, purple, black or yellow spot-like spores on the underside of leaves. Raised orange postulates will also infect the branches of the plant. The disease causes leaves to dry, twist and eventually fall off the plant.
Planting rust resistant varieties is the best way to control the disease. Good air circulation around plants will also thwart its growth and prevent leaves from staying wet for long periods of time. Swiftly remove all infected leaves from the plant to prevent its spread. Fungicides are a last resort.