First to clean it there are several commercially available cleaning products that are based on mild acids. One such is caller "CLR" (for Calcium Lime and Rust) which is not an endorsement, just an example. If the tile is ceramic, it should not harm it. Once the rust stains are gone, you should focus on why something is rusting. I can't tell from the photo what that fixture is. A grab bar of some sort? Was it designed to be mounted in a shower area? if so, it must have been cheap because they used steel, which will ALWAYS rust eventually. Sometimes people put a chrome plating on it to make it appear nice, but that never lasts. It also could be that you mounted it with steel screws, a no-no in a shower, and they are rusting BEHIND that device to where the rust is just leaking out. Either way, whatever is steel in there must be replaced with something that is brass or stainless steel, otherwise it will just happen again. When it is rusting, it is also failing and will eventually just break off.