You could, given enough time and money.
Whether it's practical or not - it's quite hard to engineer, or re-programme, a virus to target one thing specifically. Combined with the risk of mutation (what if, instead of attacking the parasite, it starts attacking white blood cells, or it finds a way to use the malarial parasite as a host, causing it to do weird things, like give off a toxic by-product of respiration).
Whilst there are "many viruses that affect us", one more would be really bad. Screwing about with genetics (which you'd pretty much have to do) can have many unfortunate side-effects which don't become apparent for a while.
Eventually, with the right technology and research, it'll be possible - but at the moment it would be an incredibly risky venture (and probably too expensive to research right now).
As to a virus spreading by itself; that is incredibly unlikely - most viruses cannot survive outside of a host environment, and die within moments of exposure to air (such as HIV) - and those that don't are usually ones that cause nasty problems in humans.