When you are assigned a task, it is because someone with authority doesn’t want to do something themselves. While you may be tempted to just perform the task, this is rarely beneficial to your career as it sends the message that you are uncreative, subservient, unimportant and, worst of all, not busy.
You could actively delegate the task by going up to someone and saying "do this". This can be effective, particularly if you are yourself in some position of authority, but keep in mind that this is exactly what has happened to you. You are in the process of shirking someone else's active delegation and there is every chance that your minion will try the same.
The most effective way to offload a task is through Passive Delegation. You know this task is important to the person who asked you to do it, otherwise they would not ask for it to be done. It is, in fact, more important to that person than it is to you. Therefore, all you need to do to passively delegate a task is to avoid doing it. Eventually the person that assigned it will give up in despair and take the task back to do themselves.
Be careful, though. When asked whether it has been done, do not say "whoops, forgot about that, let me get straight on that." Instead, tell them that the reason it isn’t done it is that you have all this important work to do (a messy desk helps here). Do not be afraid to belittle them in the process. The more snide you are about the job, the more in control you will seem. "Why would I do that when I have this to do?"
In no time at all you will be seen as too important to do anything useful and will be promoted to management.