"I'll do it soon" pretty much expresses the idea and is about as concise as you can get. I'm not sure how you could say it more briefly, other than maybe, "Yeah, soon," or simply grunting.
An appropriate statement might depend on what you mean by "soon" in context, as Robusto notes in his comment. In a business environment, "We'll have email working again soon" would be understood to mean hours at most. "We'll have the factory re-tooled to produce the new product soon" could easily mean within a few months.
Not only is there the question of how urgent the task is, but also have how soon you really plan to get to it in relation to the other person's expectations. Like, if someone wants a job done within an hour, and you plan to get to it tomorrow, "I'll get on that real soon" -- meanting tomorrow -- could be misleading. In such cases, a more specific statement might be better, like, "I'll start on that tomorrow" or "I should have that done by 3:00".