I didn't have a sign-on bonus agreemet. But the former employer claimed that I accepted their offer which has a clause saying that I shall repay the sign-on bonus if I leave voluntarily before one year. I left in about 10 months and they asked the money back.

The offer letter doesn't have my signature on it too. So my question is: is there ever an agreement between me and the company on sign-on bonus? Does the sign-on bonus clause in the offer letter have legal binding on me?

Thanks!

Yes. All they need too prove is that they have a policy on sign-on bonuses and that it was part of the offer. Since you accepted the job, you agreed to the bonus terms.

And I'll add that verbal agreements are binding.

You phrased this very carefully - did you or did you not agree to return the bonus?