On a historical basis, the Discover card requirements are the $15k annual income and a minimum FICO in the neighborhood of 690 to 700 (but that's based on feedback I hear from applicants, obviously the issuer doesn't disclose the actual qualifications to anyone).
It's worth noting that if the reason you have that score is due to limited credit history, they seem to view that more favorably then if you have it because of a charge-offs or a bankruptcy in the past (in short- they seem more open to taking a chance on those with thin credit files, as long as there isn't charged-off debt).
Here is a review of the Discover It
but I would advise against applying if your score is not in that range.
If you're a student, then try for the Discover it card for students because it's easier to get approved for. But you have to be in college in order to apply for this version.
If you don't have downright "bad" credit but it's not great either, then I would advise you check out these entry-level unsecured cards for fair credit
. A couple actually have good reward programs.