After further consideration, I'd say Rotom-C is B- rank: See edit below.
As someone who has used specially defensive Rotom-C in the past, I'd classify it as B rank (perhaps B+ or B-). It has a very nice niche of countering bulky waters, specifically Slowbro, Swampert and Alomomola while doing significant damage in return. Its typing also allows it to soak up electric attacks though it can't do much to most electric types in return. Sp. Def. Rotom-C also could have a nice niche on momentum stall, being able to pivot out with volt switch. I've found that in practice, Rotom-C is able to soak up two special attacks and pivot to a counter. Its speed tier is interesting: at base 86 uninvested, one is able to outspeed most common walls including Suicune, but very little else.
A lack of reliable recovery does hurt it significantly in a specially defensive role, and while this can be mitigated with pain split, it's still an issue. Pain Split can however, serve as a nice support option to wear down Blissey as even with full HP investment, Rotom does not have a very good HP stat for a wall. This can be bad but it also allows Rotom-C to regain full health from friendly wishes. Otherwise Rotom-C is also quite nice for its ability to spread status- specifically burns or paralysis with will-o-wisp and thunder wave which gives it nice support options on bulky offense and offense teams. It can also tank one attack from hax while crippling it with status, but that of course, would require hax not to be a lum berry variant, which it almost always is.
Leaf Storm is a powerful STAB option for hitting once but its recoil effect is quite undesirable- frankly if Rotom-C is to be used as a wall, it would prefer Giga Drain.
The inevitable comparison will come with Rotom-H. From my experience, I feel that Rotom-C has better defensive typing, resisting rock and water, although it does gain a weakness to poison and neutrality to flying. However, Rotom-H clearly has better offensive STABs as very few pokemon resist both electric and fire as Victini has demonstrated to us. Thus I'd say Rotom-C is more valuable in a supportive tank role while Rotom-H is better as a scarf/specs trick+three attacks variant.
Supporting Calcs:
Bulky Waters:
4 SpA Slowbro Scald vs. 252 HP / 252+ SpD Rotom-C: 30-36 (9.8 - 11.8%) -- possibly the worst move ever
4 SpA Slowbro Psyshock vs. 252 HP / 0 Def Rotom-C: 82-97 (26.9 - 31.9%) -- 34.4% chance to 4HKO after Leftovers recovery
vs.
4 SpA Rotom-C Leaf Storm vs. 252 HP / 0 SpD Slowbro: 354-416 (89.8 - 105.5%) -- 37.5% chance to OHKO
4 SpA Rotom-C Volt Switch vs. 252 HP / 0 SpD Slowbro: 192-228 (48.7 - 57.8%) -- 50.8% chance to 2HKO after Leftovers recovery
0 SpA Swampert Scald vs. 252 HP / 252+ SpD Rotom-C: 26-31 (8.5 - 10.1%) -- possibly the worst move ever
vs.
4 SpA Rotom-C Leaf Storm vs. 252 HP / 0 SpD Swampert: 640-756 (158.4 - 187.1%) -- guaranteed OHKO
4 SpA Alomomola Scald vs. 252 HP / 252+ SpD Rotom-C: 15-18 (4.9 - 5.9%) -- possibly the worst move ever
vs.
4 SpA Rotom-C Leaf Storm vs. 252 HP / 0 SpD Alomomola: 548-648 (102.6 - 121.3%) -- guaranteed OHKO
4 SpA Rotom-C Volt Switch vs. 252 HP / 0 SpD Alomomola: 296-350 (55.4 - 65.5%) -- guaranteed 2HKO after Leftovers recovery
Although it doesn't take much from suicune, its best bet is to go for two leaf storms and this is unreliable. However, as mentioned earlier, it can use volt switch to switch to something more capable of defeating suicune 1v1: in my team that was Toxicroak.
4 SpA Suicune Scald vs. 252 HP / 252+ SpD Rotom-C: 27-33 (8.8 - 10.8%) -- possibly the worst move ever
vs.
4 SpA Rotom-C Volt Switch vs. 252 HP / 0 SpD Suicune: 140-168 (34.6 - 41.5%) -- 69.2% chance to 3HKO after Leftovers recovery
4 SpA Rotom-C Leaf Storm vs. 252 HP / 0 SpD Suicune: 260-308 (64.3 - 76.2%) -- guaranteed 2HKO after Leftovers recovery
-2 4 SpA Rotom-C Leaf Storm vs. 252 HP / 0 SpD Suicune: 132-156 (32.6 - 38.6%) -- 1.7% chance to 3HKO after Leftovers recovery
Electric attacks:
252+ SpA Mold Breaker Mega Ampharos Thunderbolt vs. 252 HP / 252+ SpD Rotom-C: 33-39 (10.8 - 12.8%) -- possibly the worst move ever
but note:
4 SpA Rotom-C Leaf Storm vs. 252 HP / 4 SpD Mega Ampharos: 67-79 (17.4 - 20.5%) -- possible 5HKO
252 SpA Raikou Thunderbolt vs. 252 HP / 252+ SpD Rotom-C: 23-27 (7.5 - 8.8%) -- possibly the worst move ever
vs.
4 SpA Rotom-C Leaf Storm vs. 4 HP / 0 SpD Raikou: 147-174 (45.6 - 54%) -- 3.1% chance to 2HKO after Leftovers recovery
Various others:
252 SpA Hydreigon Draco Meteor vs. 252 HP / 252+ SpD Rotom-C: 142-168 (46.7 - 55.2%) -- 11.7% chance to 2HKO after Leftovers recovery (so Rotom-C can tank 2 Dracos from scarf Hydreigon while crippling with t-wave)
252 SpA Hydreigon Fire Blast vs. 252 HP / 252+ SpD Rotom-C: 160-190 (52.6 - 62.5%) -- 98.8% chance to 2HKO after Leftovers recovery
252 SpA Hydreigon Dark Pulse vs. 252 HP / 252+ SpD Rotom-C: 88-105 (28.9 - 34.5%) -- 99.6% chance to 4HKO after Leftovers recovery
252+ Atk Mold Breaker Haxorus Poison Jab vs. 252 HP / 0 Def Rotom-C: 200-236 (65.7 - 77.6%) -- guaranteed 2HKO after Leftovers recovery
That's about all I have to say for now, so let me reiterate:
Rotom-C should be B-rank for its ability to completely counter bulky waters, survive decently strong special hits (As seen with scarf hydreigon), spread status effectively, pivot with Volt Switch and recover/punish switch-ins with pain split.
It should not be more than B-rank because of bulky waters being only one niche in the meta, its lack of reliable recovery and the one-off nature of Leaf Storm, its strongest stab, which requires it to switch out the very next turn.
EDIT:
I'd like to amend my previous post by adding the fact that Rotom-C does do a good chunk to ground types like Donphan:
4 SpA Rotom-C Leaf Storm vs. 252 HP / 4 SpD Donphan: 440-518 (114.5 - 134.8%) -- guaranteed OHKO
252+ Atk Donphan Ice Shard vs. 252 HP / 0 Def Rotom-C: 86-102 (28.2 - 33.5%) -- 88.2% chance to 4HKO after Leftovers recovery
4 SpA Rotom-C Leaf Storm vs. 252 HP / 0 SpD Hippowdon: 384-452 (91.4 - 107.6%) -- 50% chance to OHKO
(Earthquake can''t touch Rotom-C)
But after further consideration, I think Rotom-C actually should be ranked B- because Rotom-H almost completely outclasses it offensively, getting far better coverage with its dual stabs (only dragon resists both electric and fire iirc) while Mew heavily intrudes on its specially defensive support role. All Rotom-C can really hold over Mew is the ability to force out bulky waters and bulky grounds (as well as not being as heavily threatened by Hydreigon) while Mew has better mixed bulk and access to instant recovery in Softboiled. Mew also keeps U-turn or Volt Switch to be able to pivot
While it does maintain a small niche of checking bulky grounds/waters Rotom-C faces tough competition from Mew and Rotom-H defensively and offensively respectively and is in many ways outclassed by them.