Thank you. Unfortunately, there is no basis for a lawsuit based on what you have described. The reason boils down to the fact that employment in the state of Alaska is "at will" absent an express agreement to the contrary. At will employment can be terminated for any reason not amounting to discrimination on the basis of a legally protected trait (race, religion, gender, etc.) or retaliation for engaging in certain forms of legally protected conduct (filing a wage claim, taking FMLA leave, etc.). It doesn't matter whether the basis for termination is fair, reasonable or even true.
So, just as your employer could have terminated you on your first day without good cause or for an unfair reason, they can terminate you before you ever start your employment. I certainly agree that your employer's stance on this issue is unreasonable, but the law just does not require them to be reasonable. Therefore, your only power here is the power of persuasion. If you can convince your employer, preferably via letter written to their HR department, that submitting for your drug test when you did should not serve as grounds for rescinding your offer, that would be your best chance at getting the job back. But you have no legal entitlement to be employed, and the company did not violate any law by rescinding their offer for this reason.
I hope that you find this information helpful and am genuinely sorry if it is not what you were hoping to hear. Please do not hesitate to let me know if you have any questions or concerns regarding the above and I will be more than happy to assist you further.
If you do not require any further assistance, please be so kind as to provide a positive rating of my service so that I may receive credit for assisting you. Very best wishes moving forward.