How did you accept the written offer? Did you sign an official employment contract? Was it an acceptance through email/phone?
You may have a claim for breach of contract. Consult with a business attorney who can go over the specific facts of your case and advise you accordingly.
You probably have no recourse. Most employees are at-will, which means that the employer can terminate at any time. Unless you and your employer signed an employment agreement that limited your employer's ability to terminate, your employer was free to change its mind regarding the new position at any time.
My answers to questions posted on AVVO are intended to provide general information only, and are not intended to be legal advice. Employment law issues typically require a careful case-by-case analysis. Consequently, if you feel that you need legal advice, I would encourage you to consult in person with an employment attorney in your area.
But you are not fired, right? You will keep your current position?
If you are an at will employee, subject to termination at the employer's will, it may not make good sense to get into a legal conflict with your employer over an in-house position that did not work out. The job you have may be better than no job and an iffy lawsuit.
No legal advice here. READ THIS BEFORE you contact me! My responses to questions on Avvo are never intended as legal advice and must not be relied upon as if they were legal advice. I give legal advice ONLY in the course of a formal attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by joint execution of a written agreement for legal services. My law firm does not provide free consultations. Please do not call or write to me with a “few questions” that require me to analyze the specific facts of your history and your license application and prescribe for you how to get a State license. Send me an email to schedule a paid Consultation for that kind of information, direction, and assistance. My law firm presently accepts cases involving State and federal licenses and permits; discipline against State and federal licenses; and disciplinary and academic challenges to universities, colleges, boarding schools, and private schools. We take cases of wrongful termination or employment discrimination only if the claims involve peace officers, universities or colleges.