James Reardon, 20, posted a video online of a man firing a gun with a caption identifying the centre in Youngstown, north of Pittsburgh, the BBC reported.
A search of his home revealed several weapons, body armour and a gas mask, police said on Sunday.
Reardon was arrested in New Middletown, near Youngstown, on Saturday and charged with menacing and harassment. He is due to appear in court on Monday.
Investigators said the alarm was raised when a post appeared on Instagram showing a man firing a gun with the caption: "Police identified the Youngstown Jewish Family Community shooter as white nationalist Seamus O'Reardon."
New Middletown Police Chief Vince D'Egidio told the media on Sunday that they believed Seamus O'Reardon was a pseudonym for James Reardon.
"He was implying that he was going to be identified as the shooter of the Jewish centre. That kicked off a very intensive investigation, a very rapidly evolving investigation," he was quoted by a local news channel as saying.
Security at Jewish facilities was increased and the FBI was contacted, D'Egidio added.
Last October, the attack on the Tree of Life Synagogue in Pittsburgh that killed 11 people, was believed to be the worst anti-Semitic attack in US history, reports the BBC.
Suspected gunman Robert Bowers has been charged with the killings and if found guilty faces life in prison without parole.
( With inputs from IANS )