It seems quite easy to queen the pawn. Let's see how this is reached:
1. c7 Rd6+ 2. Kb5!
Do not touch the c-file as you can easily see. 2. Kc5 3. Rd1 3. c8-Q Rc1+
and suddenly black is winning.
2. ... Rd5+ 3. Kb4 Rd4+ 4. Kb3 Rd3+ 5. Kc2
Now white can enter the c-file as black has no useful check on c1 now.
5. ... Rd4!
A tricky move as white cannot just queen the pawn. 6. c8-Q Rc4+! 7. Qxc4
and black is stalemate.
6. c8-R!
(see next diagram)
a
b
c
d
e
f
g
h
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
a
b
c
d
e
f
g
h
To win this game, white has to promote the pawn to a rook. This position
is a very special situation, because usally rook vs. rook is a draw, but
black's king stands too bad to survive.
White threatens mate with 7. Ra8 so black has to respond
6. ... Ra4
But now white can win the game by playing
7. Kb3
(see next diagram)
a
b
c
d
e
f
g
h
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
a
b
c
d
e
f
g
h
Now white threats to just take the rook, but at the same time white
threats to mate with 8. Rc1
Black just has no reply that could save the game.