Oral contracts can exist. If your employer can prove that you orally agreed to that term, then you could potentially be held to an oral agreement. However, if there is no evidence you agreed, then your employer will have a very hard time making that argument. The fact that your employer presented you with a written contract and you did not sign is actually good evidence that you did not agree to that term.
That being said, contract disputes like this can get surprisingly complex, and I would definitely recommend you meet with an attorney.
This foregoing answer is provided by Clay A. Alger, Esq.: (801) 478-8080. The answer provided is not intended to form an attorney client relationship and should not be construed as legal advice. Mr. Alger is licensed only in Utah.
You could have an oral contract, but in simple terms, there needs to have been an offer (the contract), and your acceptance of it. Usually, acceptance is a signature, but it could be in an email, a statement in front of witnesses, or in some cases, performing as if there was in fact an agreement. If you never indicated any acceptance of the employment agreement in any manner, then you are probably in a strong position if the employer should try to enforce it. That does not mean you can ignore the situation, and you may want to write a letter on your departure that says something like "thanks for the job" and "I never agreed to the terms of your employment agreement." How much needs to be said and the tone of the letter would depend on your situation. Like the other attorney suggests, every situation is unique, and you would do well to discuss the details of your situation directly with an attorney.
This answer or response should not be considered legal advice, and does not create an attorney-client relationship. If you have further questions, I would be glad to discuss your situation further. I can be reached at US - (801) 746-6300, or online at -- http://www.lewishansen.com/attorneys/robinson.html