The crossbench senator from the Justice Party received a US social security card while he was working in the US as a journalist in the 1960s.
He is not a US citizen and is no longer entitled to work there.
Senator Hinch said he paid around 10 years of social security tax and would have been entitled to a US pension.
But he said he wrote to the US social security department asking them to "please freeze" any pension payments after August 30 last year, when he entered parliament.
"I don’t believe a pension is a privilege," he told ABC Radio on Thursday morning.
Senator Hinch said he would seek advice from the Solicitor General, the government's lawyer, on whether his links to the US could breach Section 44 of the Constitution.
He promised to refer himself to the High Court if the advice says he may be in breach.
