John Lawler's remark (above) rightly observes that the obvious compound—angelocracy—is problematic because it amounts to saying "rule by messengers," as though James Madison were plumping for FTD florists or Western Union telegram deliverers to take over the government.
But fortunately—or fortuitously, anyway—the Christian hierarchy of angels gives us an array of leadership options based on the pecking order of angels in the cosmology. The Wikipedia article on "Christian angelology" spells out the options very neatly.
Rule by seraphim, for example, might be termed seraphocracy. However, seraph is a Hebrew word; and the closest-spelled Greek word to seraph in Liddell & Scott's Intermediate Greek–English Lexicon is σερϕος, which the dictionary defines as "a kind of gnat or winged ant." Angelic or not, a serphocracy doesn't sound like much of an upgrade over what we have now, although it might be, depending on the health insurance system the insects established. However, Wikipedia insists that the Greeks did have a suitable word for seraphim—σεραφείμ—which would make seraphocracy a legitimate option, albeit one that at its root would mean "rule by a burning one."
"Rule by cherubs" might refer to four-faced angels (man, ox, lion, and eagle) or to the toddler-like putti beloved of Renaissance painters. Wikipedia doesn't offer a Greek form of cherubim, but cherubocracy sounds pretty good until you consider that on the one hand (μεν) we have enough trouble dealing with two-faced rulers, and on the other hand (δε), as with rule by small flying insects, rule by toddlers is likely to be only slightly better than on our current form of government.
At the opposite extreme from rule by putti is rule by thrones (θρόνος is the singular Greek form). Wikipedia says that θρόνος is synonymous with "elders," but Liddell & Scott says that it means "a seat, chair" or (in Homer's day) "a throne, chair of state." So a thronocracy might refer to government by elders, or it might mean rule by an empty yet ornate chair—again not so different from what we have already.
Our next option is ophanocracy—rule by ophanim, or "wheels." In all likelihood, the ruling class's power would tend to concentrate in the hands (so to speak) of the big wheels, as is usually the case. So much for the first-sphere angels.
Leading off the second-sphere angels are the dominions or lordships—in Greek, κυριοτητες. That gives us kyriotocracy, or "rule by lordships." But English already has a term for that: feudalism.
Then come the virtues or strongholds—English translations of δυναμις, which Liddell & Scott defines as "power, might, strength." But dynamocracy sounds a bit misleading—more like "rule by TNT" than "rule by midlevel angel bureaucrats."
Rounding out the second sphere of angels are the powers or authorities—from εξουσια, which yields exousiocracy—"rule by authority," which, of course, is the form of government at English Language & Usage.
On to the third sphere of angels, where we encounter, first, principalities or rulers, from Greek αρχων, signifying "ruler," and yielding archocracy—"rule by ruler." And as a bonus, you can flip the two root words around to produce cratarchy without changing the meaning.
Then we get the archangels (ἀρχάγγελος) or "chief angels," whose government would be archangelocracy—rule by the dispatch office at Domino's Pizza. And finally, it's back to angels (again), from ἄγγελος, and angelocracy—"rule by messengers"—once more.
So the issue isn't so much "What would be the word for 'government by angels'?" as "Which of the twelve forms of angel government do you prefer?" (If I were a betting man, I would wager that citizens would vote overwhelmingly for cherubocracy because it sounds so darn cute.)