Irene Garza was last seen visiting Sacred Heart Catholic Church in McAllen, Texas where John Feit served at the time.
Ms Garza, who was Miss All South Texas Sweetheart 1958, went to confession but never returned home.
Her body was found days later. An examination found she had been raped while unconscious, beaten and suffocated.
The priest came under suspicion early on and again in 2004 but was there was insufficient evidence to charge him. He always maintained he had no involvement in her death.
It's unclear what new evidence is now being used.
"This whole thing makes no sense to me because the crime in question took place in 1960," John Feit said.
Using a walking aid and looking frail, John Feit, now 83, appeared in court in Phoenix a day after being arrested, on a murder charge. He is in custody on 750,000 dollars' bail (£517,000) while he waits to be transferred to Texas, but has vowed to fight extradition.
Speaking about the case, Hidalgo County district attorney Ricardo Rodriguez said: "The arrest of John Feit is the first step in providing justice for the murder of Ms Irene Garza.
"After nearly 56 years, Ms. Garza's family and our community will finally see that justice is served."