There is a thread elsewhere on GC that discusses minimum GPA's and the fact that it is actually not always private membership selection info. They are often posted on websites and made public. (maybe someone who is better at the search function than I am can find it?)So, by asking around, you may be able to find out that information.
Also, I would like to point out there is an "absolute, we have to get special permission to pledge below this" minimum gpa and there is the general acceptable gpa that chapters will take but are not necessarily wowed by.
Without anyone else to comment from OU - Irishpipes, maybe? - who can speak to this particular recruitment, and if this 3.8 GPA carries the weight Kstar says it does, then I suggest you focus on quality recs, quality pics, fine tuned resume, network, network, network. You never mentioned if you live near an active panhellenic alum association, but I again, want to stress that.
Okay, and one more thing,
search for threads on recs - asking for them, do's and don'ts,etc. I think that would be another good resource.