Hi and welcome to NGA! I don't have any experience with Rangoon Creeper but I'll take guess looking at your pictures.
Do you feed it? It might just be some kind of deficiency if you don't.
Worst case, it looks like it might be a fungus or bacteria .. can you by any chance wipe it off with a damp cloth or are the brown bits embedded in the leaves? Either way, your best bet is probably spraying with a fungicide.
