05AB1E, 6 bytes

DgI+FÁ

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Explanation:

D # Duplicate the text input g # Take it's length
 # i.e. "Testing..." → 10
 I # Take the integer input
 + # Add them together
 # i.e. 10 and -3 → 7
 F # Loop that many times
 Á # And rotate once towards the right during every iteration

Since 05AB1E only has builtins for Rotate once towards the right/left, and not Rotate N amount towards the right/left, I loop length + input amount of times and rotate that many times towards the right.

For example:

• "Testing..." and -3 will rotate 10 + -3 = 7 times towards the right, resulting in ting...Tes.
• "Hello world" and 5 will rotate 11 + 5 = 16 times towards the right, resulting in worldHello.

05AB1E, (削除) 6 (削除ここまで)(削除) 5 (削除ここまで) 3 bytes

(._

Inputs in the order integer,string.

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Explanation:

(  # Negate the first (implicit) input-integer
 ._ # Rotate the second (implicit) input-string that many times towards the left
  # (which supports negative integers as rotating right instead)
 # (after which the result is output implicitly)

05AB1E (legacy) , (削除) 6 (削除ここまで) 5 bytes

sg+FÁ

Inputs in the order integer,string.

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Explanation:

s # Swap so the two (implicit) inputs are in reversed order on the stack
 g # Pop and push the length of the top input-string
 + # Add it to the input-integer
  F # Loop that many times
 Á # And rotate once towards the right during every iteration
 #  (using the last implicit input-string in the first iteration)

Since the legacy version of 05AB1E only has builtins for Rotate once towards the right/left, and not Rotate \$n\$ amount towards the right/left, I loop \$length + input\$ amount of times and rotate that many times towards the right.

For example:

• "Testing..." and -3 will rotate \10ドル + -3 = 7\$ times towards the right, resulting in ting...Tes.
• "Hello world" and 5 will rotate \11ドル + 5 = 16\$ times towards the right, resulting in worldHello.

The new version of 05AB1E does have a builtin for rotating \$n\$ amount of times towards the left, which is ._, saving 2 bytes .

#05AB1E , 6 bytes

DgI+FÁ

Try it online or verify all test cases.

Explanation:

D # Duplicate the text input
 g # Take it's length
 # i.e. "Testing..." → 10
 I # Take the integer input
 + # Add them together
 # i.e. 10 and -3 → 7
 F # Loop that many times
 Á # And rotate once towards the right during every iteration

Since 05AB1E only has builtins for Rotate once towards the right/left, and not Rotate N amount towards the right/left, I loop length + input amount of times and rotate that many times towards the right.

For example:

• "Testing..." and -3 will rotate 10 + -3 = 7 times towards the right, resulting in ting...Tes.
• "Hello world" and 5 will rotate 11 + 5 = 16 times towards the right, resulting in worldHello.

05AB1E , 6 bytes

DgI+FÁ

Try it online or verify all test cases.

Explanation:

D # Duplicate the text input
 g # Take it's length
 # i.e. "Testing..." → 10
 I # Take the integer input
 + # Add them together
 # i.e. 10 and -3 → 7
 F # Loop that many times
 Á # And rotate once towards the right during every iteration

Since 05AB1E only has builtins for Rotate once towards the right/left, and not Rotate N amount towards the right/left, I loop length + input amount of times and rotate that many times towards the right.

For example:

• "Testing..." and -3 will rotate 10 + -3 = 7 times towards the right, resulting in ting...Tes.
• "Hello world" and 5 will rotate 11 + 5 = 16 times towards the right, resulting in worldHello.