The unidentified airman has been given until November to change his mind or he will be forced out.
The current oath used by the USAF ends with "so help me God".
Previously, the airmen had signed but crossed out the ending. He was told on 25 August that this meant it would not be accepted.
The American Humanist Association (AHA) has taken up the case and insists the airman should be allowed to swear a secular oath.
An AHA attorney, Monica Miller, has said the airmen will sue if not allowed to re-enlist.
She said: "The government cannot compel a nonbeliever to take an oath that affirms the existence of a supreme being.
"Numerous cases affirm that atheists have the right to omit theistic language from enlistment or reenlistment contracts.
"This Airman shows integrity, commitment to the nation, and respect for religion in standing firm for a secular oath that reflects his true values and intentions."
American law requires the contested phrase to included but implementation is left to the discretion of each branch.
The omission of the phrase was allowed until October last year when updated Air Force instructions dropped the option.
The USAF has said it cannot make any changes unless changes to the statute mandating the oath are approved by Congress.
A spokesperson for the USAF, Rose Richeson, said the Defense Department’s General Counsel has been consulted to review the rule.
The full oath reads...
I, [insert name], do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; and that I will obey the orders of the President of the United States and the orders of the officers appointed over me, according to regulations and the Uniform Code of Military Justice. So help me God.