The internal auditor’s role often includes helping to set corporate objectives and the design and monitoring of performance measures,
The above statement is correct.
my question is: set corporate objectives should be the responsibility of the company management or the board of directors, is the internal auditor have the role of setting the objectives?
I think it would be unusual for IA to set corporate objectives. As you say, this is the job of the directors.
IA might get involved in devising how progress in achieving corporate should be measured. Effective measurement is important and IA may subsequently audit the reported performance measures.