Perhaps, but it probably wouldn't be a good idea.
Firstly, from a practical point of view: you would likely need to have summoned your Patronus ahead of time, since my understanding is that when first summoned it is only a sort of mist and requires a few seconds to take full corporeal form. In most cases, your adversary is unlikely to allow you the time to do this, and if they do, it would probably be easier and safer to disapparate.
Even if your Patronus is already present, it isn't clear how quickly and precisely the wizard can control its actions - getting it to jump in front of you at just the right time might be challenging. (Admittedly, this would not be as much of a problem if you have a large Patronus like Harry's.)
More importantly, it seems to me that a Patronus is a corporeal representation of your inner being. If it is corporeal enough to block Avada Kedavra, it is corporeal enough to be affected by it, and it seems very likely that this would have a severe effect on you. (It seems even more likely that Avada Kedavra would be unable to affect a Patronus, but in that case it wouldn't be blocked by one, either.)
Absolute best case scenario, it would destroy the happy memory you used to cast it (which might be worth it if it saves your life) but it seems more likely that it would cripple you severely enough that death would be preferable - perhaps you would lose the ability to ever be happy, for example, or perhaps it would outright destroy your soul. (The latter is my guess, given the relationship between the Patronus spell and Dementors.)
Given the risks involved, I doubt that anyone has been willing to experiment. So this is probably an unresolved question, even from an in-universe perspective.