APL (Dyalog Unicode), 15 bytes

Full program, prompting for input via stdin. The structure is an anonymous infix function which due to the shifting gets either 10 or 100 or 1 as its right argument. The (optional) left argument of 0 or nothing or 00 is ignored. Then we divide the right argument by 10 giving us 1 or 10 or 0.1 and find the 10-logarithm of that, giving us 0 or 1 or -1. Finally we prompt for input and shift by that amount.

--- 0{⍞⌽⍨10⍟⍵÷10}10

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{…} anonymous infix function where ⍵ is the right argument; 10

⍵÷10 divide the right argument by ten; 1

10⍟ log₁₀ of that; 0

…⌽⍨ cyclically rotate the following by that number of steps:

⍞ stdin

{⍞⌽⍨10⍟⍵÷10}100 

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{…} anonymous infix function where ⍵ is the right argument; 100

⍵÷10 divide the right argument by ten; 10

10⍟ log₁₀ of that; 1

…⌽⍨ cyclically rotate the following by that number of steps:

⍞ stdin

--- 00{⍞⌽⍨10⍟⍵÷10}1

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{…} anonymous infix function where ⍵ is the right argument; 0

⍵÷10 divide the right argument by ten; 0.1

10⍟ log₁₀ of that; -1

…⌽⍨ cyclically rotate the following by that number of steps:

⍞ stdin

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