Build me a castle Stairway!
05AB1E, 12 bytes
Code:
vDNúsÀ}\».B∞

Uses the 05AB1E encoding. Try it online!
Explanation:
v     }        # Length input times, do.. (N = iteration count)
 DNú           #   Duplicate and prepend N spaces
    sÀ         #   Swap and rotate one to the left
       \       # Discard the top of the stack
        »      # Join the stack by newlines
         .B    # Pad with spaces into a rectangle
           ∞   # Mirror the string