Yes you can paint it, but you will want to go through a few steps to make sure that the paint adheres. First you will need to pressure wash the siding to remove dirt and oxidized paint. If the oxidation (also called “Chalking”) is really bad this may take a while, and using TriSodium Phosphate (TSP) will help, though this is mostly applied by hand thus takes longer than the pressure washing. Be careful with the pressure washer as if you are too close or are using a zero degree tip (which you ought not use in this application) then you can harm the siding.
Once the siding is clean and the surface sound (run your hand across it.. if the paint comes off as dust on your hands, it still needs more cleaning) you can prime the surface with a good primer. I would recommend a alkyd, shellac, or alcohol based primer. Once this is done, and you have allowed for the appropriate dry time, you can top coat it with a quality paint. This is one of those times where spending more money on the product will save you money. If you have it available in your area I would strongly recommend the Manor Hall line of paints from Pittsburgh Paints. As a painting and remodeling contractor I have worked with most paints at one point or another and I have found that Manor Hall is heads and shoulders above the rest for durability, coverage, and ease of application.
Apply at least two top coats of paint, even if the first covers or seems to cover. The added life of the paint job will save you time and money in the long run.