The answer is "yes, but..." Two principles apply. First, mutual mistakes are not enforceable against the mistaken author of a contract; courts will generally "reform" such agreements to reflect the true intention of the parties. Assuming your employer can demonstrate that the parties' agreement was not really as reflected in the offer, then the offer will not be enforced as written.
But there is a larger, more important problem (part two): employment in the United States is on an "at will" basis, which means that either party may unilaterally terminate the arrangement at any time for any reason or no reason at all. Unless your offer contains a "duration" term, your employer can terminate it, or unilaterally alter it, at any time. You have no remedy.
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