What you have written would be understood; but the reference is the fact of someone giving a testimonial, or the testimonial itself. The person is a referee - though many employers/employment agencies use 'reference' to mean 'the name and address of someone who is prepared to write a testimonial'.
That said, sometimes people are unhappy about using 'referee' for this purpose. I'd say something like '...would you give me a reference' or 'can I give people your name for a reference'.
Student or Learner