You posted a different position after my comment and PhishMaster's answer.
As for the new position, yes it is mate in 7 starting with Rxc1+.
Possible continuations are:
Kd2 Rc2+ 2. Ke1 (if 2. Ke3 Re2++; if 2. Kd1 Nf3+ 3. Rd7 Rxd7++) Nf3+ 4. Rxf3 Bxf3 (threat is Rd1++) 5. Re8+ Rxe8 6. Kf1 Bg2+ 7. Kg1 Re1++
Kf2 Rc2+ 2. Kg1 (if 2. Ke1 or Ke3 see the other line above) Nf3+ 3. Rxf3 (3. Kh1 Rxh2++) Rd1+ 4. Rf1 Rg2+ 5. Kh1 Rxf1++
As I wrote above the mating patterns are not particularly pretty. It boils down (in the longer lines) to mating with two rooks, one on the second and one on the first rank. Also it is more like a mate in 5 as some of the moves are just white sacrificing a rook to prolong the mate.