The former minister faces 26 charges in Poland in connection with the Justice Fund, a government program originally intended to support crime victims.
Prosecutors allege that the fund was misused for political purposes during his tenure.
Ziobro denies wrongdoing and says the case is politically motivated.
He said he intends to meet members of the Polish diaspora in Washington and insisted he had not fled Poland.
Ziobro added that he was using a document issued in connection with international protection granted to him while in Hungary.
Polish authorities invalidated his passport last year.
The Polish foreign ministry said on Tuesday it had sent a diplomatic note to the US embassy in Warsaw requesting clarification on the legal basis for his entry into the United States.
The US State Department declined to comment on the details of his entry, citing the confidentiality of visa records.
Ziobro's stay in Hungary came under the government of then-Prime Minister Viktor Orbán.
Orbán's successor, Péter Magyar, said during the election campaign that Polish politicians sought by prosecutors would face extradition.
TV Republika has said Ziobro will work for the outlet as a political commentator in the United States.
Poland's National Public Prosecutor's Office said investigators are examining whether others may have helped Ziobro evade criminal liability or obstruct the Justice Fund probe.
National Public Prosecutor Dariusz Korneluk said prosecutors had summoned Tomasz Sakiewicz, CEO and editor-in-chief of TV Republika, as a witness.
Prosecutors want Sakiewicz to explain Ziobro's role at the station and whether it could be linked to aiding a suspect in evading justice.
Ziobro said TV Republika had offered him a commentator's role several times over the past year and that he accepted after deciding to travel to the United States.
"TV Republika has a large audience and strong influence among Polish Americans," he said.
Ziobro, who served as justice minister during PiS's time in power, is accused by prosecutors of leading an organized criminal group and abusing his office. He rejects the allegations.
A Polish court is considering a request to issue a European arrest warrant for Ziobro.
Another PiS politician, Marcin Romanowski, a former deputy justice minister, is also a suspect in the Justice Fund investigation.